Introduction To Trigonometry Questions

We provide introduction to trigonometry practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on introduction to trigonometry skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

Introduction To Trigonometry Questions

List of introduction to trigonometry Questions

Question NoQuestionsClass
1In rectangle ( A B C D, ) diagonal ( B D=26 mathrm{cm} ) and cotangent of angle ( A B D=1.5 . ) Flnd the area and the perimeter of the rectangle ABCD
A. Area = 436 sq. cm and perimeter = ( 11 sqrt{13} mathrm{cm} )
B. Area = 842 sq. cm and perimeter = ( 15 sqrt{13} mathrm{cm} )
c. Area ( =312 ) sq. ( mathrm{cm} ) and perimeter ( =20 sqrt{13} mathrm{cm} )
D. Area = 231 sq. cm and perimeter = ( 12 sqrt{13} mathrm{cm} )
10
2Using Trigonometric functions of ( frac{boldsymbol{pi}}{boldsymbol{4}} )
Find the value of ( sin frac{pi}{8}=? )
10
369. If tan (20 + 45°) = cot 30 where
(20 + 459) and 30 are acute an-
gles, then the value of 0 is
(1) 5°
(2) 9°
(3) 12 (4) 15°
10
4Which one of the following relations is
true?
( A cdot cos ^{2} Theta-sin ^{2} Theta=1 )
B. ( operatorname{cosec}^{2} Theta-sec ^{2} Theta=1 )
( mathbf{c} cdot cot ^{2} Theta-tan ^{2} Theta=1 )
( mathrm{D} cdot sec ^{2} Theta-tan ^{2} Theta=1 )
10
5Express the following in terms of trigonometric ratios of angles lying
between 0 and ( 45^{circ} )
( sec 76^{circ}+operatorname{cosec} 52^{circ} )
10
6If ( sin theta=frac{7}{25} ) and ( 90^{0}<theta<180^{0}, ) then
find the value of ( sec theta+tan theta )
10
73. Solve the equation sinx – cos? x =10
858. Find the value of:
cos70° cos55° cosec 35°
sin20° tan5º tan25º tan 45º
tan 65º tan 85°
(1) 1
(2) 2
(3) 3
(4) 4
10
968.
If tan a = n tan ß and sin a = m
sin B, then cosa a is
m2 +1
m2-1
n2-1
n2+1
10
10tan
A cot A
14. The expression -cot A ‘ 1-tan A
can be written as:
[JEE M 2013)
(a) sinA COSA +1
(b) SecA cosecA +1
(C) tanA + cotA
(d) secA + cosecA
10
1170. The value of cosec2 32° – tan
58° is
(1) O
(2) 2
(3) -1
(4) 1
10
12Find ( boldsymbol{theta}, ) if ( boldsymbol{0} leq boldsymbol{theta} leq mathbf{9 0}^{boldsymbol{o}} )
( sqrt{boldsymbol{3}} tan boldsymbol{theta}=mathbf{1} )
10
1324. A right triangle has perimeter of length 7 and hypotenuse
of length 3. If @ is the larger non-right angle in the
triangle, then the value of cos e equals
ſo -√2
b. 4 + 2
6
4-√2
C.-3
4-√2
C.
10
14Find the value of ( x ) :
( sec ^{2} 2 x=1-tan 2 x )
10
15Find ( theta ) when
( sin theta+operatorname{cosec} theta=1 )
10
16Refer the above figure and find the
value of ( sec n )
A ( cdot sqrt{5} )
B. ( 2 sqrt{5} )
c. ( frac{sqrt{5}}{2} )
D. ( frac{sqrt{5}}{5} )
E. ( frac{2 sqrt{5}}{5} )
10
17If ( sin (alpha+beta)=1 ) and ( sin (alpha-beta)=1 / 2 )
where ( boldsymbol{alpha}, boldsymbol{beta} boldsymbol{epsilon}[mathbf{0}, boldsymbol{pi} / 2] ) then
This question has multiple correct options
A ( cdot tan (alpha+2 beta)=-sqrt{3} )
B. ( tan (2 alpha+beta)=-1 / sqrt{3} )
( mathbf{c} cdot tan (alpha+2 beta)=sqrt{3} )
D. ( tan (alpha+2 beta)=1 / sqrt{3} )
10
18If ( sec theta=2 x ) and ( y tan theta=2, ) then the
value of ( 2left[x^{2}-frac{1}{y^{2}}right] ) is
( mathbf{A} cdot mathbf{1} )
B. ( frac{1}{2} )
( c cdot frac{1}{3} )
D.
10
1955.
will be
tan 3A – tan 2A -tan A
tan 3A. tan 2A. tan A
equal to
(1) O
(2)
(4) 1
10
20cot? A
65. The expression 1+1+cosec A
is equal to
(1) cosec A
(3) cos A
(2) sin A
(4) tan A
10
21then the
68. If cost o – si
value of 1 – 2 sin’e is
(1)
(2) O
10
22Find the value of ( boldsymbol{theta}, ) if
( tan theta=sqrt{3} )
10
23( ln triangle A B C, angle B=90^{circ}, B C=7 ) and
( A C-A B=1, ) then ( cos C=dots )
A ( cdot frac{3}{25} )
в. ( frac{6}{25} )
( c cdot frac{7}{25} )
D. ( frac{8}{25} )
10
24If ( sin A=frac{3}{5} ) and ( A ) is not in the first quadrant then find ( frac{cos A+sin 2 A}{tan A+sec A} )
A ( cdot frac{16}{25} )
в. ( frac{17}{25} )
c. ( frac{22}{25} )
D. ( frac{19}{25} )
10
2561. sinº 5° + sin²6° + … + sin? 84°
+ sina 85º = ?
(1) 39
(3) 40
(2) 40
(4) 397
10
26If ( frac{sin A}{sin B}=frac{sqrt{3}}{2} ) and ( frac{cos A}{cos B}=frac{sqrt{5}}{2}, 0< )
( A, B<frac{pi}{2}, ) then find the value of
( tan A+tan B )
A ( cdot frac{sqrt{5}-sqrt{3}}{sqrt{3}} )
B. ( frac{sqrt{5}-sqrt{3}}{sqrt{5}} )
c. ( frac{sqrt{3}+sqrt{5}}{sqrt{5}} )
D. ( frac{sqrt{3}+sqrt{5}}{sqrt{3}} )
10
27If ( operatorname{cosec} theta-sin theta=a^{3} ) and ( sec theta- )
( cos theta=b^{3}, ) prove that ( a^{2} b^{2}left(a^{2}+b^{2}right)=1 )
10
2866. If sin 21° =
. then sec 21° –
sin 69° is equal to
work
(2) xvy? – x?
10
29( cos A=a cos B, sin A=b sin B Rightarrow )
( left(b^{2}-a^{2}right) sin ^{2} B= )
A ( cdot 1+a^{2} )
B ( cdot 2+a^{2} )
c. ( 1-a^{2} )
D. ( 2-a^{2} )
10
30If ( a^{2} sec ^{2} theta-b^{2} tan ^{2} theta=c^{2} ) then prove
( operatorname{that} sin ^{2} theta=frac{c^{2}-a^{2}}{c^{2}-b^{2}} )
10
31Solve:
( csc ^{2} theta cdot tan ^{2} theta-1=tan ^{2} theta )
10
32Prove that:
( left[1+cot theta-sec left(theta+frac{pi}{2}right)right][1+cot theta+sec )
( 2 cot theta )
10
33If ( sec C ) is ( frac{m}{2 sqrt{2}}, ) then ( m ) is:
( A )
B
( c )
10
34If ( k=tan 25^{circ} ) then find ( frac{k-1}{k+1}+frac{k+1}{k-1} )
A. 2 ( operatorname{cosec} 130^{circ} )
B . 2 ( operatorname{cosec} 45^{circ} )
c. ( 2 sec 130^{circ} )
D. ( 2 sec 400^{circ} )
10
35If ( 24 cot A=7, ) find the value of ( sin A )10
36Solve ( sqrt{3} sec 2 theta=2 )10
37If ( tan A+cot A=2 ) then find the value
of ( tan ^{2} A+cot ^{2} A )
10
3855. If A, B, C are the angles of a A
ABC then following is equal to:
sin (B+C)
(1) cos Â
(3) cosec
(2) sec
(4) sec
10
3972. If 3sin’e – cos0 = 1, then find
the value of sin 0.
(3) 1
(4) 2
10
40Prove that ( : frac{1-tan ^{2}left(45^{circ}-Aright)}{1+tan ^{2}left(45^{circ}-Aright)}=sin 2 A )10
41If ( sin theta=frac{7}{25}, ) where ( theta ) is an acute, find
the value of ( cos theta ) using identity
10
4251. If sina + cosß = a and cosa + sin
B = b then what will be the value
a² +6²
a sin a + bcos a
(1) – 1 (2) + 1
(3) – 2 (4) +2
of –
10
43If ( A ) and ( B ) are acute angles such that
( sin A=sin ^{2} B, 2 cos ^{2} A=3 cos ^{2} B )
then
This question has multiple correct options
( A cdot A=frac{pi}{6} )
B. ( A=frac{pi}{2} )
c. ( B=frac{pi}{4} )
D. ( B=frac{pi}{3} )
10
44If ( boldsymbol{p}=cos boldsymbol{x}-sin boldsymbol{x}, boldsymbol{q}=frac{1-sin ^{3} boldsymbol{x}}{1-sin boldsymbol{x}}, boldsymbol{r}= )
( frac{1+cos ^{3} x}{1+cos x} )
What is the value of ( p+q+r ? )
( A cdot O )
B.
( c cdot 2 )
D. 3
10
45( operatorname{Let} theta inleft(0, frac{pi}{4}right) ) and ( t_{1}=(tan theta)^{tan theta}, t_{2}= )
( (tan theta)^{cot theta}, t_{3}=(cot theta)^{tan theta} operatorname{then} t_{4}= )
( (cot theta)^{cot theta}, ) then
A ( cdot t_{1}<t_{2}<t_{1}t_{1}>t_{3}>t_{4} )
c. ( t_{3}>t_{1}>t_{2}>t_{4} )
D. ( t_{2}>t_{3}>t_{1}>t_{4} )
10
46n the following figure, ( tan ^{2} boldsymbol{A}-sec ^{2} boldsymbol{A} )
( A )
3. -2
( c )
( D )
10
47If ( sin A=frac{3}{5}, ) and ( cos A=frac{4}{m}, ) then ( m ) is10
48( mathrm{IF} tan Theta=frac{8}{15} ) then the value of
( frac{17 sin Theta+frac{5}{cos theta}}{5 tan Theta+frac{8}{sin theta}} )
A ( cdot frac{59}{41} )
в. ( frac{35}{41} )
c. ( frac{41}{59} )
D. ( frac{41}{35} )
10
49Solve ( frac{sin theta+cos theta}{sin theta-cos theta}+frac{sin theta-cos theta}{sin theta+cos theta}= )
( frac{2 sec ^{2} theta}{tan ^{2} theta-1} )
10
50If ( cos B=frac{1}{3}, ) find the other five
trigonometric ratios
10
5168. The minimum value of 2 sin2 0+
3 cos2 O is
(1) O
(2) 3
(3) 2
(4) 1
10
52cose
63. If
cota e-cos20
0° <0 < 90°, then the value of
is :
(1) 30°
(2) 45°
(3) 60°
(4) None of these
10
5366. In A POR, 29 is a right angle,
PO = 3 and QR = 4. If ZP = Q and
ZR = B. then tan B = ?
(1)
10
5411. If sin 0 = , then cos @ will be10
5567. If cosa sinº a
cos B sin28 = 1 then
sin*a + sin“ß = ?
(1) 2sin’a.sin B
(2) sin’a. sin?
(3) sina. sinß
(4) 2sina. sinß
10
56If ( 0 leq x, y leq 180^{circ} ) and ( sin (x-y)= )
( cos (x+y)=frac{1}{2}, ) then the values of ( x )
and ( y ) are given by This question has multiple correct options
A. ( x=45^{circ}, y=15^{circ} )
В. ( x=45^{circ}, y=135^{circ} )
c. ( x=165^{circ}, y=15^{circ} )
D. ( x=165^{circ}, y=135^{circ} )
10
57n figure, ( A C=13 mathrm{cm}, B C=12 mathrm{cm}, ) then
( sec theta ) equals:
A ( cdot frac{13}{12} )
B. ( frac{5}{12} )
c. ( frac{12}{13} )
D. ( frac{5}{13} )
10
5869. The value of sin cos 0 tan Ocot
O sec 0 cosec O is
(1) O
(2) 1
(3) 2
(4) Undefined
@ Undefine
10
5969. If 3 tan 0 = 4, then the value of
4 sino-3 cos e
3sine + 2 cose is
10
60If ( cos (beta-gamma)+cos (gamma-alpha)+cos (alpha- )
( beta)=-frac{3}{2}, ) then
This question has multiple correct options
A. ( sum cos alpha=0 )
B. ( sum sin alpha=0 )
c. ( sum cos alpha sin alpha=0 )
D. ( sum(cos alpha+sin alpha)=0 )
10
6170. If o be acute angle and cos 0
15
17. then the value of
cot (90°-) is
10
62If ( tan theta=frac{1}{sqrt{2}}, ) find the value of ( frac{operatorname{cosec}^{2} theta-sec ^{2} theta}{operatorname{cosec}^{2} theta+cot ^{2} theta} )
A ( cdot frac{1}{10} )
в. ( frac{2}{10} )
( c cdot frac{3}{10} )
D. ( frac{4}{10} )
10
6351. If sina + cosß = a and cosa + sin
B = b then what will be the value
of
a + b2
a sin a + bcos a’
(1) – 1 (2) + 1
(3) – 2 (4) + 2
10
64Find ( A ) if ( tan 49^{circ}=cot A )10
6574. If tan
tano + coto
= 2,0505 90°),
-cote
then the value of sin 0 is
(3)
(4) 1
(4) 1
10
66n ( triangle A B C ),right angled at ( B, A B+ ) ( boldsymbol{A C}=mathbf{9} ) cm and ( boldsymbol{B C}=mathbf{3} boldsymbol{c m} )
The value of ( sec C ) is
( A cdot frac{4}{3} )
B.
( c cdot frac{1}{3} )
D. none
10
6713. Which of the following has value zero?
(a) sin 0°
(b) tan 0°
(c) cos 0°
(d) cot 0°
10
68Express the following in terms of trigonometric ratios of angles lying
between 0 and 45:
( tan 65^{0}+cot 49^{0} )
10
69(ii)10
70( sin A=frac{4}{5}, A ) being an acute angle. Find
the value of ( 2 tan A+3 sec A+ )
( 4 sec A cdot csc A )
10
71then cos will be
(c) 2^2
10 MI+
10
7272. The value of
1
+
sin? 23°
cos23°
(1) 2
(3) 1
cos? 67° cosec 67°
sin2 67° sec? 230
mm (2) 0
(4) -1
10
73Without using tables, prove the following ( sin 40^{circ}-cos 70^{circ}=sqrt{3} )
( cos 80^{circ} )
10
7465. If (sin a + cosec a)2 + (cos a +
sec a) = k + tan’a + cot’a, then
the value of k is
(1) 1
(2) 7
(3) 3
(4) 5
10
75The given relation is ( (1+tan a+ )
( cos a)(sin a-cos a)=2 sin a tan a- )
cat ( a cos a )
A. True
B. False
10
76In triangle ( P Q R ), right angled at ( Q ), if ( tan P=frac{1}{sqrt{3}} ) find the value of ( sin P+ )
( cos R+cos P sin R )
10
77The expression ( (tan Theta+sec theta)^{2} ) is
equal to
A ( cdot frac{1+cos Theta}{1-cos 0} )
B. ( frac{1+sin Theta}{1-sin 0} )
c. ( frac{1-cos Theta}{1+cos 0} )
D. ( frac{1-sin Theta}{1+sin Theta} )
10
78Prove that ( (1+cot A+tan A)(sin A- )
( cos A)=sin A tan A-cot A cos A )
10
7971. If OSO
71. rosostane = r
tan
=
then cos 6 =
10
8070. The value of (tan35° tan45°
tan559) is
(1)
(2) 2
(3) O
(4) 1
10
81Evaluate :
( sin left(90^{circ}-Aright) sin A-cos left(90^{circ}-right. )
( A) cos A )
10
8270. In an acute angled triangle ABC,
if sin 2(A + B-C) = 1 and tan (B
+C-A) = 3, then the value of
ZB is
(1) 60°
(2) 30°
(3) 52
(4) 67
10
83What is ( sin ^{2} 20^{circ}+sin ^{2} 70^{circ} ) equal to?
( mathbf{A} cdot mathbf{1} )
B. 0
( c cdot-1 )
D.
10
84Find the value of ( sin frac{pi}{18} sin frac{5 pi}{18} sin frac{7 pi}{18} )10
85Prove that ( : frac{tan Theta}{1-cot Theta}+frac{cot Theta}{1-tan Theta}=1+ )
( tan Theta+cot Theta )
10
8672. If tano
7 and dis acute, then
cosec 0
ܠܛ |
ܗ | ܠܕ
10
87Simplify ( frac{sin 35^{circ}}{cos 55^{circ}}+frac{cos 55^{circ}}{sin 35^{circ}}-2 cos ^{2} 60^{circ} )10
8861. If (A+B+C) = 25 then sin(S – A)
+ sin (S-B) + sin (S-C) -sin S
will be equal to
A B C
(1) 4 sin sin, sin
(2) 2 sinA sinB sinc
10
89If ( a sin ^{3} x+b cos ^{3} x=sin x cos x ) and
( a sin x=b cos x ) then ( a^{2}+b^{2}= )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
D. 3
10
9065. If tan a = p, then
sec a + tan? a. cosec a =
2
p3
(1) (1 + p2j3/2
(2) Son2
(3 VI+p2
(4) Vi+p
10
91If ( cos x+cos ^{2} x=1, ) prove that ( sin ^{2} x+ )
( sin ^{4} x=1 )
10
9212. Which of the following has value 1:
(a) tan 45º
(b) sin 90°
(c) cos 90°
(d) cos 0°
10
93Prove the following identity :
( (1+tan alpha tan beta)^{2}+(tan alpha- )
( tan beta)^{2}=sec ^{2} alpha sec ^{2} beta )
10
94In ( triangle A B C, ) right angled at ( B, A B=10 )
and ( A C=26 . ) Find the six
trigonometric ratios of the angles ( A ) and ( C )
10
95Prove ( sin ^{2} frac{pi}{8}+sin ^{2} frac{3 pi}{8}+sin ^{2} frac{5 pi}{8}+ )
( sin ^{2} frac{7 pi}{8}=2 )
10
96In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios. ( tan theta=11 )10
97Given right triangle ( boldsymbol{R} boldsymbol{S} boldsymbol{T} ) in figure
calculate the length of ( overline{S T} ), to the
nearest hundredth. (Use ( cos 42^{0}= )
( mathbf{0 . 7 4 3 2}) )
( mathbf{A} cdot 12.04 m m )
B. ( 13.38 mathrm{mm} )
c. ( 16.21 mathrm{mm} )
D. 24.22 ( m m )
E ( .26 .90 m m )
10
98( frac{cos (90-theta) sec (90-theta) tan theta}{operatorname{cosec}(90-theta) sin (90-theta) cot (90-theta)} )
( frac{tan (90-theta)}{cot theta}=dots )
( A )
B. –
( c cdot 2 )
D. -2
10
9971. If tan e =
then the value of
3sin 0+2 cos
3sin 0-2 cos is
(1) 0.5
(2)-0.5
(3) 3.0 (4) -3.0
10
100The value of ( sin ^{2} alpha+operatorname{cosec}^{2} alpha ) is always
A. greater than 1
B. less than 1
c. greater than or equal to 2
D. equal to 2
10
10169. If seco + tano = 2, then the
value of sec O is
(1) (2) 5
(3) 7 (4) 5
10
102( ln a Delta A B C, ) if ( cos A cos B cos C=frac{sqrt{3}-1}{8} )
and ( sin A sin B sin C=frac{3+sqrt{3}}{8}, ) then
The value of ( tan A tan B+tan B tan C+ )
( tan C tan A ) is
10
103Prove the following
( 1 .left(1-sin ^{2} Aright) sec ^{2} A=1 )
( 2 . sec ^{4} theta-sec ^{2} theta=tan ^{4} theta+tan ^{2} )
3. ( (sec theta-tan theta)^{2}=frac{1-sin theta}{1+sin theta} )
4. ( frac{tan theta+sec theta-1}{tan theta-sec theta+}=frac{1+sin theta}{cos theta} )
10
10467. If cos e + sin 0 = 12 cos 0, then
cos 0 -sin is
(1) 2 tane
(2) – 2 cos e
(3) – 12 sino
(4V2 sino
10
105Find ( boldsymbol{m} ) if ( operatorname{cosec} boldsymbol{C} ) is equal to ( frac{mathbf{5}}{m} )10
10615. Let fx(x) = (sink x+cos* x) where xeR and k 21.
Then f1(x)- fo (x) equals
(JEE M 2014]
10
107If the ratio of the height of tower and the length of its shadow is ( 1: sqrt{3} ), then the
angle of elevation of the sum has
measure
A . ( 60^{circ} )
B . ( 45^{circ} )
( c cdot 30^{circ} )
D. ( 75^{circ} )
10
10869. If sin a + cos B = 2 (Oºs B<as
en sin
90°), then sin (2017) –
(1) sin Ž (2) cos
(3) sin
10
109Find the values of ( cos theta ) and ( tan theta, ) given ( sin theta=frac{8}{17} ) and ( theta ) is in quadrant 110
110( left{29 cos theta=20, text { find } sec ^{2} theta-tan ^{2} thetaright. )10
111If ( boldsymbol{x}=sin (boldsymbol{alpha}-boldsymbol{beta}) cdot sin (gamma-boldsymbol{delta}) ; boldsymbol{y}= )
( sin (beta-gamma) cdot sin (alpha-delta) ) and ( z= )
( sin (gamma-alpha) cdot sin (beta-delta,) ) then
A. ( x+y+z=0 )
в. ( x+y-z=0 )
c. ( y+z-x=0 )
D. None of these
10
112( mathrm{IF} cos theta=frac{3}{5}, ) then the value of
( frac{sin theta tan theta+1}{2 tan ^{2} theta} ) is
A ( cdot frac{88}{160} )
в. ( frac{91}{160} )
c. ( frac{92}{160} )
D. ( frac{93}{160} )
10
113Find the value of ( x ) in the following:
( cos 2 x=cos 60^{circ} cos 30^{circ}+ )
( sin 60^{circ} sin 30^{circ} )
10
114If the angle of elevation of a cloud from a point h meters above a lake is ( alpha ) and
the angle of depression of its reflection in the lake is ( beta ) then height of the cloud is ( hleft(frac{1+r}{1-r}right) ) where ( r=frac{text { tan } alpha}{tan beta} )
A. True
B. False
10
11569. If x sec20 + y cosec?0 = 4xy and
x sino – y cos 0 = 0, then x – y
will be equal to
(1) -1
(2) +1
(3) O
(4) xy
10
116( fleft(frac{1+sin theta-cos theta}{1+sin theta+cos theta}right)^{2}= )
( lambdaleft(frac{1-cos theta}{1+cos theta}right), ) then ( lambda ) equals
( A )
B. 1
( c cdot 2 )
D.
10
117In the following figure, in
( triangle A B C, B C=1, A C=2, angle B=90^{circ} )
Find the value of ( sin theta )
10
118If ( boldsymbol{x}=boldsymbol{p} sec boldsymbol{theta} ) and ( boldsymbol{y}=boldsymbol{q} tan boldsymbol{theta}, ) then
( mathbf{A} cdot x^{2}-y^{2}=p^{2} q^{2} )
B . ( x^{2} q^{2}-y^{2} p^{2}=p q )
c. ( x^{2} q^{2}-y^{2} p^{2}=frac{1}{p^{2} q^{2}} )
D . ( x^{2} q^{2}-y^{2} p^{2}=p^{2} q^{2} )
10
119Prove ( sec ^{4} x-sec ^{2} x=tan ^{4} x+tan ^{2} x )10
12069. If A = tan 11°tan 29°,
B = 2 cot 61° cot 79′, then :
(1) A = 2B (2) A = -2B
(3) 2A =B (4) 2A = – B
10
121In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios. ( cos theta=frac{7}{25} )10
122( frac{3+cot 76^{0} cot 16^{0}}{cot 76^{0}+cot 16^{0}} ) is equal to
This question has multiple correct options
( A cdot tan 16^{0} )
B ( cdot cot 76^{0} )
( mathbf{C} cdot tan 46^{circ} )
( mathbf{D} cdot cot 44^{0} )
10
123If ( boldsymbol{x}=boldsymbol{y} cos frac{boldsymbol{2} boldsymbol{pi}}{boldsymbol{3}}=boldsymbol{z} cos frac{boldsymbol{4} boldsymbol{pi}}{boldsymbol{3}}, ) then ( boldsymbol{x} boldsymbol{y}+ )
( boldsymbol{y} boldsymbol{z}+boldsymbol{z} boldsymbol{x}= )
A . -1
B. 0
c. 1
D. 2
10
124Express ( sin 12 theta+sin 4 theta ) as the product
of sines and cosines.
10
12566. The value of 0, which satisfies
the equation tan²0 + 3 = 3 seco,
0° < < 90° is
(1) 15° or 0° (2) 30° or 0°
(3) 45° or 0 (4) 60° or 0°
10
126Evaluate
( frac{sin ^{2} 63+sin ^{2} 27}{cos ^{2} 27+cos ^{2} 63} )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot-1 )
D.
10
127If ( tan A=frac{5}{12}, ) find the value of ( (sin A+ )
( cos A) times sec A: )
A ( cdot frac{6}{13} )
в. ( frac{7}{12} )
c. ( frac{17}{12} )
D. ( frac{12}{17} )
10
128Without using trigonometric tables,find the value of the following:
( left(frac{tan 20^{circ}}{operatorname{cosec} 70^{circ}}right)^{2}+left(frac{cot 20^{circ}}{sec 70^{circ}}right)^{2}+ )
( 2 tan 15^{circ} tan 45^{circ} tan 75^{circ} )
10
12967. If 3 sin + 5 cos 0 = 5, then the
value of 5 sin 0-3 cos 0 will be
(1) + 3 (2) + 5
(3) + 2 (4) + 1
10
13010. cos (30°) is equal to
(d) None
10
131( frac{cot theta-cot 2 theta}{cot theta} ) is equal to
( mathbf{A} cdot frac{x}{z} )
( mathbf{B} cdot frac{y}{z} )
( mathbf{c} cdot frac{y}{x} )
D. ( frac{x}{y} )
10
13270. If (secA + tana) (secB + tanB)
(secC + tan C) = (secA -tan A)
(secB-tanB) (secC- tanC), then
each one is equal to
(1) 1
(2) -1
(3) + 1 (4) O
10
133If ( cos Theta_{1}+cos Theta_{2}+cos Theta_{3}=3, ) find
( sin Theta_{1}+sin Theta_{2}+sin Theta_{3} )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
D. 3
10
134Find ( P Q, ) if ( A B=150 m, angle P=30^{circ} )
and ( angle Q=45^{circ} )
.978 .8
8
3,524.4
( c .279 .9 )
D. 409.8
10
135If ( sec 2 A=operatorname{cosec}left(A-42^{circ}right) ) where ( 2 A )
is acute angle, then value of ( A ) is
A ( cdot 44 )
B ( .22^{circ} )
( c cdot 21^{circ} )
D. ( 66^{circ} )
10
136( frac{2 tan 45^{circ}}{1+tan ^{2} 45^{circ}} )10
137If ( sin theta+cos theta=sqrt{2} cos theta, ) then the
general value of ( boldsymbol{theta} ) is
10
138If ( tan ^{2} theta=left(1-e^{2}right) ) then ( sec theta+ )
( tan ^{3} theta operatorname{cosec} theta ) is equal to
A ( cdotleft(2+e^{2}right)^{frac{3}{2}} )
B. ( left(2-e^{2}right)^{frac{3}{2}} )
c. ( left(1-e^{2}right)^{frac{3}{2}} )
D. ( left(1+e^{2}right)^{frac{3}{2}} )
10
139The value of
( tan 5^{circ} tan 10^{circ} tan 15^{circ} cdots tan 85^{circ} ) is
( A cdot 0 )
B. not defined
( c cdot 1 )
D. –
10
140If ( operatorname{cosec} theta=2 x ) and ( y cot theta=2, ) then the
value of ( 4left(x^{2}-frac{1}{y^{2}}right) ) is :
( A )
B. ( frac{1}{2} )
( c cdot frac{1}{3} )
D.
10
141( ln triangle A B C ) prove that ( frac{b-C}{a}= )
( frac{tan (B / 2)-tan (C / 2)}{tan (B / 2)+tan (C / 2)} )
10
142( boldsymbol{x}= )
( operatorname{cosec}left(tan ^{-1}left(cos left(cot ^{-1}left(sec left(sin ^{-1} aright)right)right)right.right. )
( sec left(cot ^{-1}left(sin left(tan ^{-1}left(operatorname{cosec}left(cos ^{-1} aright)right)right)right.right. )
where ( a in[0,1] . ) Then which of the
following options is correct?
A ( cdot x^{2}+a^{2}=3 )
В. ( x=y )
c. ( y^{2}+a^{2}=3 )
D. All of these
10
143If ( triangle A B C ) is right angled at ( B ) and
( B C=7 c m, A C-A B=1 mathrm{cm}, ) then
find the value of ( cos A+sin A )
10
144( ln Delta A B C, A B=8 mathrm{cm}, A C=5 mathrm{cm} ) and
( boldsymbol{m} angle boldsymbol{A}=mathbf{5 0}^{circ} . ) Then
(a) What is the length of the perpendicular from ( C ) to ( A B ? )
(b) Find the length of BC ( left[sin 50^{circ}=0.7660, cos 50^{circ}=right. )
( 0.6428, ) tan50 ( ^{circ}=1.1918 )
10
145( cos ^{-1}left(2 x^{2}-1right), 0 leq x leq 1, ) is equal to10
146x
10.
1
10. irsiy scope, then
Cost
If Sin *

then
(2009)
8
sin
(C)
tan
=
8
27
125
10
147Area of the field is
( mathbf{A} cdot a^{2} sin alpha cos alpha+c^{2} sin beta cos beta+e^{2} sin gamma cos gamma )
B. ( (a cos alpha+c cos beta+d+e cos gamma)(a sin alpha+b+c sin beta+ )
( e sin gamma) )
C ( cdot a^{2}+b^{2}+c^{2}+d^{2}+e^{2} )
D. none of these
10
14872. If 8 sin²0 – 10 sino + 3 = 0, then
what will be value of sino from
the following?
(2) TO
the circle at
10
14967. If x = a cos (90° – 0) and y =
b cot (90° – 0), then the value of
(1) 2
(3) 1
(2) – 1
(4) 0
10
15013
72. If sec?0 + tan²0 =
then the value of sec 0 – tanto is
12.
(1) 12
(2) 1
(3) 0
(4) 3
10
151A circus artist is climbing a ( 20 m ) long
rope, which is tightly stretched and tied from the top of a vertical pole of the
ground. Find the height of the pole if the angle made by the rope with the ground
level is ( 30^{circ} )
A . ( 12 mathrm{m} )
B. 10
( c cdot 8 m )
( D cdot 6 m )
10
152If ( angle A ) and ( angle B ) are acute angles such
that ( cos A=cos B ) then prove that
( angle A=angle B )
10
153The value of ( tan 203^{circ}+tan 22^{circ}+ )
( tan 203^{circ} tan 22^{circ} ) is
A . -1
B. 0
c. 1
D. 2
10
154tande
70.
sec 0 + 1 – sec 0 is equal to
(1) 1
(2) O
(3) -1 (4) None of these
10
155( f sin left(7 phi+9^{circ}right)=cos 2 phi, ) find a value of
( phi )
10
156In ( triangle A B C, ) angle ( A ) is ( 120^{circ}, B C+C A=20 )
and ( A B+B C=21 . ) Find the length of the
side BC.
10
15767. If tan o. cos 60° = then
the value of sin (0 -15°) is
-la
(3) 1
(4) T
10
15864. sine + cos6 O is equal to
(1) 1
(2) 1-3 sincos20
(3) 1 – 3 sin cos 0
(4) 1 + 3 sina o cosa
10
159if ( sin theta=frac{4}{5}, ) Find the value of ( frac{4 tan theta-5 cos theta}{sec theta+4 cot theta} )10
160In triangle ( A B C ), the medians intersect
at point ( G . ) Suppose ( angle A B C=90^{circ} ) and
( angle B A C+angle B G C=180^{circ} . ) Find the value
of ( cos angle A C B )
A ( cdot frac{sqrt{2}}{sqrt{3}} )
B. ( frac{sqrt{2}}{sqrt{5}} )
c. ( frac{2}{sqrt{5}} )
D. None of these
10
161Prove the following
( sec theta(1-sin theta)(sec theta+tan theta)=1 )
10
1620
From the following figure, ( tan C ) is ( frac{1}{m} )
The value of ( boldsymbol{m} ) is:
10
163In right triangle ( A B C, B C=7 c m )
( boldsymbol{A C}-boldsymbol{A B}=mathbf{1 c m} ) and ( angle boldsymbol{B}=mathbf{9 0}^{circ} . ) The
value of ( cos A+cos B+cos C ) is
A ( cdot frac{1}{7} )
в. ( frac{32}{24} )
c. ( frac{31}{25} )
D. ( frac{25}{31} )
10
164Ab is ( 47.32 mathrm{cm} )
f true then enter 1 and if false then
enter 0
10
165Prove that, ( (cos alpha+cos beta)^{2}+ )
( (sin alpha+sin beta)^{2}=4 cos ^{2}left(frac{alpha-beta}{2}right) )
10
166Prove that:
[
sin 38^{circ}+sin 22^{circ}=sin 82^{circ}
]
10
167If ( sin theta+sin ^{2} theta+sin ^{3} theta=1, ) then the
value of ( cos ^{6} theta-4 cos ^{4} theta+8 cos ^{2} theta )
must be-
10
16872. The value of
cos 2 60°+ 4 sec 30°-tan2 45°
sin 30°+ cos2 30°
10
16951. The value of the following is
(sin 47° 2 (cos 43°) 2
(cos 43°) (sin 47°) – 4cos2450
(1) -1 (2) 0
(3) 1
10
170( cos 45^{circ} cdot tan (-495)^{circ}- )
( tan 585^{circ} cdot cot left(-495^{circ}right)=0 )
10
171Express the trigonometric ratios
( sin A, sec A ) and ( tan A ) in terms of ( cot A )
( ^{mathbf{A}} cdot sin A=frac{1}{sqrt{cot A+1}} )
( sec A=frac{sqrt{cot ^{2} A-1}}{cot A} )
( tan A=frac{1}{cot A} )
B. ( sin A=frac{1}{sqrt{cot ^{2} A+1}} )
( sec A=frac{sqrt{cot ^{2} A+1}}{cot A} )
( tan A=frac{1}{cot A} )
( ^{mathrm{C}} cdot sin A=frac{1}{sqrt{cot A-1}} )
( sec A=frac{sqrt{cot ^{2} A+sin A}}{cot A} )
( tan A=frac{1}{cot A} )
D. None of these
10
172< 90°
64. If tan 0 + cot 0 = 2,0<
then the value of O is
(1) 75° (2) 30°
(3) 45° (4) 60°
10
173Solve for ( boldsymbol{x}:-boldsymbol{a} boldsymbol{r} sin frac{boldsymbol{5}}{boldsymbol{x}}+boldsymbol{a r c} sin frac{boldsymbol{1} boldsymbol{2}}{boldsymbol{x}}= )
( frac{pi}{2} )
10
174What is ( frac{cot 54^{circ}}{tan 36^{circ}}+frac{tan 20^{circ}}{cot 70^{circ}} ) equal to?
( A cdot 0 )
B. 1
( c cdot 2 )
D.
10
17551. The value of the following:
sin 47° 2 (cos 43° 2
(cos 43º) (sin 47°) – 4c052450
(1) -1
(2) 0
(3)
1
145
10
176( tan ^{2} phi-sin ^{2} phi=tan ^{2} phi cdot sin ^{2} phi )10
177f a line makes ( alpha, beta, gamma, delta ) angles with 4
diagonals of a cube, then ( cos ^{2} alpha+ )
( cos ^{2} beta+cos ^{2} gamma+cos ^{2} delta=? )
( mathbf{A} cdot mathbf{1} )
B.
( c cdot frac{4}{3} )
D.
10
17865.
tan A tan B tan(A – B)
tan A-tan B-tan(A – B)
be equal to
(1) tan (A + B)
(2) tan 45º
(3) tan (45 + A)
(4) tan (A-B)
10
179If ( angle A ) and ( angle B ) are acute angles such
that ( cos A=cos B, ) then show that ( angle boldsymbol{A}=angle boldsymbol{B} )
10
180Prove that a triangle ( A B C ) is equilateral
if and only if ( tan A+tan B+tan C= )
( mathbf{3} sqrt{mathbf{3}} )
10
181Solve ( cos ^{2} x^{3} )10
18267. The value of
sin o is
1
coseco-coto
(1) 1
(3) cosec 0
(2) coto
(4) tan 0
10
183Prove the following:
If ( tan A=frac{3}{4}, ) then ( sin A cos A=frac{12}{25} )
10
184Find all values of ( theta ) satisfying the equation ( sin theta=sin theta+sin 3 theta, ) where
( mathbf{0} leq boldsymbol{theta} leq boldsymbol{pi} )
10
185Which of the following values are possible?

This question has multiple correct options
( mathbf{A} cdot sin theta=0 )
в. ( sec theta=frac{1}{2} )
( mathbf{c} cdot tan theta=1 )
D. ( operatorname{cosec} theta=sqrt{3} )

10
186Show that ( sqrt{frac{1-cos A}{1+cos A}}=frac{sin A}{1+cos A} )10
187If ( pi<alpha<2 pi ) then
( frac{1}{sin alpha-sqrt{cot ^{2} alpha-cos ^{2} alpha}}= )
( A cdot sin alpha )
B. – ( sin alpha )
c. ( frac{1}{sin alpha} )
( D )
10
188In the following, one of the six trigonometric ratios is given. Find the
values of the other trigonometric ratios. ( sin theta=frac{sqrt{3}}{2} )
10
189( sin 36^{circ} sin 72^{circ} sin 108^{circ} sin 144^{circ}= )
( A cdot 1 / 4 )
B. 1/16
( c cdot 3 / 4 )
D. 5/16
10
190If ( sin theta=frac{12}{13}, ) find the value of ( frac{sin ^{2} theta-cos ^{2} theta}{2 sin theta cos theta} times frac{1}{tan ^{2} theta} )10
191If ( tan theta cdot tan phi=sqrt{frac{(a-b)}{(a+b)}}, ) then
( (a-b cos 2 theta)(a-b cos 2 phi)= )
A ( cdot a^{2} )
в. ( b^{2} )
( mathbf{c} cdot a^{2}+b^{2} )
D. ( a^{2}-b^{2} )
10
192If ( tan theta=frac{4}{7}, ) then ( frac{7 sin theta-3 cos theta}{7 sin theta+3 cos theta}= )
A ( cdot frac{1}{7} )
в.
( c cdot frac{3}{7} )
D. ( frac{5}{14} )
10
193If ( tan theta+sec theta=4, ) then find ( sin theta+ )
( cos theta )
A .
B. – –
c. ( frac{23}{17} )
D. ( frac{13}{14} )
10
19419. For any o f the expression
3(sino-cos)* +6(sino + cose)2 + 4sin equals:
[JEEM 2019-9 Jan (M)
(a) 13-4cos20 + 6sincos²0
(b) 13-4cose
(c) 13-4cos20 + 6cose
(d) 13-4cos40 +2sin20cos20
10
195If ( 4 x=csc theta & frac{4}{x}=cot theta, ) find the value
of ( 4left[x^{2}-frac{1}{x^{2}}right] )
10
196L
If x = a seca cosß, y = b seca
sinß, z = c tan a, then the value
x2 y2 22
а
(2) O
(3) 1
(4) -1
(1) 2
10
197If ( a sin ^{2} theta+b cos ^{2} theta=c, ) then ( tan ^{2} theta= )
A ( cdot frac{b-c}{a-c} )
в ( cdot frac{c-b}{a-c} )
c. ( frac{a-c}{b-c} )
D. ( frac{a-c}{c-b} )
10
198( x=frac{sin ^{3} p}{cos ^{2} p}, y=frac{cos ^{3} p}{sin ^{2} p} ) and ( sin p+cos p )
( =frac{1}{2} ) then ( x+y= )
A ( cdot frac{75}{18} )
в. ( frac{44}{9} )
c. ( frac{79}{18} )
D. ( frac{48}{9} )
10
199( ln a Delta A B C, ) if ( cos A cos B cos C= )
( frac{sqrt{3}-1}{8} ) and ( sin A . sin B . sin C= )
( frac{mathbf{3}+sqrt{mathbf{3}}}{mathbf{8}} )
then- ( 0 n ) the basis of above information, answer the following questions:The
value of ( tan A+tan B+tan C ) is:
A ( frac{3+sqrt{3}}{sqrt{3}-1} )
B. ( frac{sqrt{3}+4}{sqrt{3}-1} )
c. ( frac{6-sqrt{3}}{sqrt{3}-1} )
D. ( frac{sqrt{3}+sqrt{2}}{sqrt{3}-1} )
10
20066. If 5 cos 0 + 12 sin 0 = 13, then
tan 0 =
10
201Type your question
List-I
[
begin{array}{l}text { List-II } \ text { I) } cos x=-frac{1}{2} & text { a) } mathrm{x}=frac{7 pi}{3}end{array}
]
( begin{array}{ll}text { II) } sin x=frac{sqrt{3}}{2} & text { b) } x=frac{7 pi}{6} \ text { ( } | text { ) } tan x=sqrt{3} & text { c) } x=frac{8 pi}{3}end{array} )
( A cdot b, d, c, a )
( B cdot c, a, b, e )
( mathbf{C} cdot b, c, e, a )
( mathbf{D} cdot b, e, e, a )
10
202What is the value of ( sec ^{2}left(tan ^{-1}left(frac{5}{11}right)right) ? )
A . ( 121 / 96 )
B. 217/921
( c cdot 146 / 121 )
D. 267/121
10
203In right triangle ( E D F ) is figure, the
length of ( overline{D F} ) is ( 2 mathrm{cm}, ) and the length of EF is ( 7 mathrm{cm} ). Calculate the measure of
( angle E F D, ) to the nearest hundredth of a
degree. (Use ( left.sin 73.4^{0}=0.9583right) )
( mathbf{A} cdot 15.95^{circ} )
в. ( 16.6^{circ} )
( c cdot 73.40^{circ} )
D. ( 90^{circ} )
E . 99.9
10
20473. The value of
tan 4°.tan 43°tan 47°.tan 86° is
(1) 2
(2) 3
(3) 1
(4) 4
10
205Prove that: ( sin ^{2} A cos ^{2} B- )
( cos ^{2} A sin ^{2} B=sin ^{2} A-sin ^{2} B )
10
20671. The value of
(1 + tan20)
(1 + cot? e) IS
(1)
(2) 1
(3) 2
10
207The value of ( sin 0^{circ} ) is
A. 0
B. ( frac{1}{2} )
c. ( frac{sqrt{3}}{2} )
D.
10
208If ( A ) and ( B ) are acute angles such that
( sin A=sin ^{2} B, 2 cos ^{2} A=3 cos ^{2} B )
then
This question has multiple correct options
A ( cdot A=frac{pi}{6} )
B. ( A=frac{pi}{2} )
c. ( B=frac{pi}{4} )
D. ( B=frac{pi}{3} )
10
209Assertion
Statement ( 1: cos 1<sin 1(text { in } text {radians}) )
Reason
Statement 2: cosine x decreases but
sine ( x ) increases for ( x inleft(0, frac{pi}{2}right) )
A. Both the statements are TRUE and STATEMENT 2 is the
correct explanation of STATEMENT 1
B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1.
C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.
10
210If ( sin theta=frac{8}{17} ) and ( 90^{circ}<theta<180^{circ}, ) then
the value of the expression ( frac{2 sin theta+cos theta}{3 cos theta+5 sin theta} ) is :
( A cdot frac{1}{5} )
B. ( -frac{1}{5} )
c. ( frac{31}{85} )
D. ( -frac{31}{85} )
10
211If ( cos theta=frac{1}{3}, ) then ( tan theta= )
begin{tabular}{l}
A ( cdot 2 sqrt{2} ) \
hline
end{tabular}
B. 2
( c cdot sqrt{2} )
D. None of above
10
21272. The value of (sin 20°. cos 70° +
cos 20° sin 70°) is:
(1) 1
(2) O
(3) – 1
(4)
10
213Find the value of ( cos 210^{circ} sin 300^{circ} )10
214n the Fig. ( 8.12 angle R ) is the right angle of
( Delta P Q R ) write the following ratios.
(i) ( sin P )
(ii) ( cos Q )
(iii) ( tan mathrm{P} )
(iv) ( tan mathrm{Q} )
10
21570. If sin (A-B) = sin A cos B-COSA
sinB, then sin 15° will be
3+1
272
(2) 212
3-1
13-1
-V2
22
10
216Find the value of ( : cot ^{2} C-frac{1}{sin ^{2} C} )
( A ldots )
B
( r )
10

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