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JEE • MATHEMATICS • COMPOUND ANGLES

Compound angles practice · Mixed difficulty

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 61-90 of 147 questions
61 Easy
61 of 147
Application +4 | -1
If sin⁡(α+β)=1,sin⁡(α−β)=1/2\sin (\alpha+\beta)=1, \sin (\alpha-\beta)=1 / 2 then tan⁡(α+2β)tan⁡(2α+β)\tan (\alpha+2 \beta) \tan (2 \alpha+\beta) is equal if α,β\alpha, \beta are acute angle
View answer and explanation
Correct option: A
1
Option D (π3\frac{{\pi}}{{3}} or 2π3\frac{{2 \pi}}{{3}}) is correct because solving the infinite geometric series and then finding the angle whose sine is 32\frac{{\sqrt{{3}}}}{{2}} gives these two solutions within the specified range.
62 Easy
62 of 147
Application +4 | -1
tan⁡  80∘−tan⁡  10∘tan⁡  70∘\frac{{\tan \,\,80^\circ - \tan \,\,10^\circ }}{{\tan \,\,70^\circ }} is equal to
View answer and explanation
Correct option: C
2\mathrm{2}
Option C (2) is correct because it is obtained by using the tangent subtraction formula and trigonometric identities.
63 Easy
63 of 147
Application +4 | -1
If 0<θ<π40 < \theta < \frac{\pi}{4} then sec⁡2θ−tan⁡2θ\sec 2 \theta-\tan 2 \theta is equal to
View answer and explanation
Correct option: C
tan⁡(π4−θ)\tan \left(\frac{\pi}{4}-\theta\right)
Option C (tan⁡(π4−θ)\tan \left(\frac{\pi}{4}-\theta\right)) is correct because simplifying the given expression using trigonometric identities leads to this result.
64 Easy
64 of 147
Analyzing +4 | -1
If θ=2π7\theta=\frac{2 \pi}{7}, then the value of tan⁡θtan⁡2θ+tan⁡2θtan⁡4θ+tan⁡4θtan⁡θ\tan \theta \tan 2 \theta+\tan 2 \theta \tan 4 \theta+\tan 4 \theta \tan \theta is
View answer and explanation
Correct option: D
-7
Option D (-7) is correct. By substituting θ=A,2θ=B,4θ=C\theta = A, 2\theta = B, 4\theta = C and using trigonometric identities, the expression simplifies to -7.
65 Easy
65 of 147
Application +4 | -1
If cos⁡(θ−α)=α,  cos⁡(θ−β)=b,   then  sin⁡2  (α−β)+2  ab  cos⁡  (α−β)  \cos \left( {\mathrm{\theta } - \alpha } \right) = \alpha ,\,\,\cos \left( {\mathrm{\theta } - \beta } \right) = b,\,\;\mathrm{then}\,\,{\sin ^2}\,\,\left( {\alpha - \beta } \right) + 2\,\,ab\,\,\cos \,\,\left( {\alpha - \beta } \right)\mathrm{\;} is equal to

View answer and explanation
Correct option: A
a2+b2{a^2} + {b^2}
Option A (a2+b2{a^2} + {b^2}) is correct because by using trigonometric identities and the given conditions, the expression simplifies to a2+b2{a^2} + {b^2}.
66 Medium
66 of 147
Application +4 | -1
tan⁡5π12−tan⁡π12−3tan⁡5π12tan⁡π12\tan \frac{5 \pi}{12}-\tan \frac{\pi}{12}-\sqrt{3} \tan \frac{5 \pi}{12} \tan \frac{\pi}{12} is equal to
View answer and explanation
Correct option: D
3\sqrt{3}
Option D (3\sqrt{3}) is correct because using the tangent subtraction formula, the expression simplifies to tan⁡(5π12−π12)=tan⁡(π3)=3\tan(\frac{5\pi}{12} - \frac{\pi}{12}) = \tan(\frac{\pi}{3}) = \sqrt{3}.
67 Medium
67 of 147
Application +4 | -1
If acos⁡3θ+3acos⁡θsin⁡2θ=xa \cos ^3 \theta+3 a \cos \theta \sin ^2 \theta=x and asin⁡3θ+3acos⁡2θsin⁡θ=ya \sin ^3 \theta+3 a \cos ^2 \theta \sin \theta=y, then (x+y)2/3+(x−y)2/3=(x+y)^{2 / 3}+(x-y)^{2 / 3}=
View answer and explanation
Correct option: A
2a2/32 a^{2 / 3}
Option A (2a2/32 a^{2 / 3}) is correct because simplifying the given equations and using the binomial theorem leads to this result.
68 Medium
68 of 147
Application +4 | -1
If CC is an obtuse angle in tringle, then
View answer and explanation
Correct option: A
tan⁡Atan⁡B<1\tan A\tan B < 1
The correct answer is A (tan⁡Atan⁡B<1\tan A\tan B < 1) because if C is obtuse, then A+B is acute, and the tangent of an acute angle is positive.
69 Easy
69 of 147
Application +4 | -1
sin⁡250+sin⁡210∘+sin⁡215∘+…….+sin⁡290∘=\sin ^{2} 5^{0}+\sin ^{2} 10^{\circ}+\sin ^{2} 15^{\circ}+\ldots \ldots .+\sin ^{2} 90^{\circ}=
View answer and explanation
Correct option: C
9129 \frac{1}{2}
Option C (9 1/2) is correct because pairing terms using the identity sin2(x) + sin2(90-x) = 1 simplifies the sum, and accounting for the remaining terms leads to the correct result.
70 Medium
70 of 147
Analyzing +4 | -1
If cos⁡  (θ−α)=a,  cos⁡(θ−β)=b\cos \,\,\left( {\theta - \alpha } \right) = a,\,\,\cos \left( {\theta - \beta } \right) = b, then sin⁡2(α−β)+2 ab  cos⁡(α−β)={\sin ^2}\left( {\alpha - \beta } \right) + 2\,ab\,\,\cos \left( {\alpha - \beta } \right) =
View answer and explanation
Correct option: A
a2+  b2{a^2} + \,\,{b^2}
Option A (a2+  b2{a^2} + \,\,{b^2}) is correct because the trigonometric identity and given equations simplify to this expression.
71 Hard
71 of 147
Application +4 | -1
If cos⁡  20∘−sin⁡  20∘=p\cos \,\,20^\circ - \sin \,\,20^\circ = p, then cos⁡  40∘\cos \,\,40^\circ is equal to
View answer and explanation
Correct option: B
p 2−p2p\,\sqrt {2 - {p^2}}
Option B (p2−p2p\sqrt{2 - p^2}) is correct because by squaring the given equation and manipulating trigonometric identities, we can express cos⁡40∘\cos 40^\circ in terms of pp.
72 Easy
72 of 147
Application +4 | -1
If cos⁡(α+β)=35,  sin⁡(α−β)=513\cos (\alpha + \beta ) = \frac{3}{5},\,\,\sin (\alpha - \beta ) = \frac{5}{{13}} and 0<α,  β<π4, 0 < \alpha ,\,\,\beta < \frac{\pi }{4},\, then tan⁡(2α)\tan (2\alpha ) is equal to
View answer and explanation
Correct option: B
6316\frac{{63}}{{16}}
Option B is correct because it accurately calculates the value of tan⁡(2α)\tan(2\alpha) using the given trigonometric values and the tangent addition formula.
73 Easy
73 of 147
Analyzing +4 | -1
The value of 3cot⁡  20∘−4cos⁡  20∘\sqrt 3 \cot \,\,20^\circ - 4\cos \,\,20^\circ is
View answer and explanation
Correct option: A
1
Option A is correct because the expression simplifies to 1 after applying trigonometric identities and simplifications.
74 Easy
74 of 147
Application +4 | -1
If in a   in  a   Δ  ABC,   ∠C=90∘\mathrm{\;in\;a\;}\,\Delta \mathrm{\;}ABC,\,\;\angle C = 90^\circ, then the maximum value of sin⁡  A  sin⁡  B   is\sin \,\,A\,\,\sin \,\,B\;\,\mathrm{is}

View answer and explanation
Correct option: A
12\frac{1}{2}
Option A (12\frac{1}{2}) is correct because the maximum value of sin⁡Asin⁡B\sin A \sin B is found using trigonometric identities and the fact that A+B=90∘A + B = 90^\circ.
75 Easy
75 of 147
Application +4 | -1
The value of tan⁡  5θ\tan \,\,5\theta is
View answer and explanation
Correct option: A
5  tan⁡  θ−10  tan⁡3  θ+tan⁡5  θ1−10  tan⁡2  θ+5  tan⁡4  θ\frac{{5\,\,\tan \,\,\theta - 10\,\,{{\tan }^3}\,\,\theta + {{\tan }^5}\,\,\theta }}{{1 - 10\,\,{{\tan }^2}\,\,\theta + 5\,\,{{\tan }^4}\,\,\theta }}
Option A (5 tan⁡ θ−10 tan⁡3 θ+tan⁡5 θ1−10 tan⁡2 θ+5 tan⁡4 θ\frac{{5\,\tan \,\theta - 10\,{{\tan }^3}\,\theta + {{\tan }^5}\,\theta }}{{1 - 10\,{{\tan }^2}\,\theta + 5\,{{\tan }^4}\,\theta }}) is correct because it represents the expansion of tan⁡5θ\tan 5\theta using the multiple angle formula.

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SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
76 Easy
76 of 147
Analyzing +4 | -1
The value of tan⁡  20∘+2tan⁡  50∘−tan⁡  70∘\tan \,\,20^\circ + 2\tan \,\,50^\circ - \tan \,\,70^\circ, is
View answer and explanation
Correct option: B
0
Option B (0) is correct because the trigonometric expression simplifies to zero using trigonometric identities.
77 Medium
77 of 147
Application +4 | -1
If cos⁡  θ=817\cos \,\,\theta = \frac{8}{{17}} and θ\theta lies in the first quadrant, then the value of cos⁡  (30∘+θ)+cos⁡  (45∘−θ)+cos⁡  (120∘−θ)\cos \,\,\left( {30^\circ + \theta } \right) + \cos \,\,\left( {45^\circ - \theta } \right) + \cos \,\,\left( {120^\circ - \theta } \right), is
View answer and explanation
Correct option: A
2317  (3−12+12)\frac{{23}}{{17}}\,\,\left( {\frac{{\sqrt 3 - 1}}{2} + \frac{1}{{\sqrt 2 }}} \right)
Option A is correct because it correctly uses trigonometric identities and the given cosine value to simplify the expression and find the final value.
78 Easy
78 of 147
Application +4 | -1
Find the value of xx if x=1−4sin⁡10∘sin⁡70∘2sin⁡10∘x=\frac{1-4 \sin 10^{\circ} \sin 70^{\circ}}{2 \sin 10^{\circ}}.
View answer and explanation
Correct option: A
1
Option A (1) is correct because simplifying the expression using trigonometric identities leads to the value of 1.
79 Easy
79 of 147
Application +4 | -1
The value of     cos⁡  12∘−sin⁡  12∘cos⁡  12∘+sin⁡  12∘+  sin⁡  147∘cos⁡  147∘  \;\;\frac{{\cos \,\,12^\circ - \sin \,\,12^\circ }}{{\cos \,\,12^\circ + \sin \,\,12^\circ }} + \;\frac{{\sin \,\,147^\circ }}{{\cos \,\,147^\circ }}\; is equal to
View answer and explanation
Correct option: C
0\mathrm{0}
Option C (0) is correct because simplifying the expression using trigonometric identities leads to the result of 0.
80 Medium
80 of 147
Application +4 | -1
An angle α\alpha is divided into two parts so that the ratio of the tangents of these parts is λ\lambda. If the difference between these parts is xx then sin⁡x/sin⁡α\sin x / \sin \alpha is equal to
View answer and explanation
Correct option: C
λ−1λ+1\frac{\lambda-1}{\lambda+1}
Option C, λ−1λ+1\frac{\lambda-1}{\lambda+1}, is correct because it directly follows from applying the tangent subtraction and addition formulas and then using the sine subtraction and addition formulas.
81 Easy
81 of 147
Application +4 | -1
If sin⁡  θ=1213,      (0<θ<π2)\sin \,\,\theta = \frac{{12}}{{13}},\,\,\;\;\left( {0 < \theta < \frac{\pi }{2}} \right) and cos⁡  ϕ=−35(π<ϕ<3  π2)\cos \,\,\phi = - \frac{3}{5}\left( {\pi < \phi < \frac{{3\;\pi }}{2}} \right), then sin⁡  (θ+ϕ)\sin \,\,\left( {\theta + \phi } \right) will be
View answer and explanation
Correct option: B
− 56/65- \,56/65
Option B (− 56/65-\,56/65) is correct because it is the result of applying the sine addition formula and substituting the given values.
82 Easy
82 of 147
Application +4 | -1
If A+B=45∘A + B = 45^\circ, then (cot⁡A−1)(cot⁡B−1)\left( {\cot A - 1} \right)\left( {\cot B - 1} \right) is equal to
View answer and explanation
Correct option: D
2
Option A (2) is correct because substituting A + B = 45° into the cotangent addition formula and simplifying leads to the result (cot A - 1)(cot B - 1) = 2.
83 Easy
83 of 147
Application +4 | -1
If tan⁡A=2tan⁡B+cot⁡B\tan A = 2\tan B + \cot B, then 2tan⁡(A−B)2\tan \left( {A - B} \right) is equal to
View answer and explanation
Correct option: C
cot⁡B\cot B
Option C is correct because it represents the simplified expression for 2tan⁡(A−B)2\tan(A-B) after substituting the given value of tan⁡A\tan A.
84 Easy
84 of 147
Application +4 | -1
cosec    15∘+sec⁡  15∘cosec\;\,\,15^\circ + \sec \,\,15^\circ is equal to
View answer and explanation
Correct option: C
2 62\,\sqrt 6
Option C (2 62\,\sqrt 6) is correct because it is the simplified value of the expression after converting to sine and cosine and using trigonometric values.
85 Medium
85 of 147
Application +4 | -1
The smallest positive values of xx and yy which satisfy tan⁡(x−y)=1,  sec⁡(x+y)=23\tan \left( {x - y} \right) = 1,\,\,\sec \left( {x + y} \right) = \frac{2}{{\sqrt 3 }} are
View answer and explanation
Correct option: A
x=25   π24,  y=7  π24x = \frac{{25\,\;\pi }}{{24}},\,\,y = \frac{{7\;\pi }}{{24}}
Option A (x=25  π24,, y=7  π24x = \frac{{25\;\pi }}{{24}},\\,\,y = \frac{{7\;\pi }}{{24}}) is correct because it provides the smallest positive values of x and y that satisfy both given trigonometric equations.
86 Easy
86 of 147
Application +4 | -1
The value of 1cos⁡  290∘  +  13  sin⁡  250∘\frac{1}{{\cos \,\,290^\circ }}\,\, + \,\,\frac{1}{{\sqrt 3 \,\,\sin \,\,250^\circ }} is equal to
View answer and explanation
Correct option: D
4/34/\sqrt 3
Option D (4/34/\sqrt 3) is correct because it results from simplifying the given trigonometric expression using trigonometric identities.
87 Medium
87 of 147
Application +4 | -1
If cot⁡αcot⁡β=2\cot \alpha \cot \beta=2, then cos⁡(α+β)cos⁡(α−β)\frac{\cos (\alpha+\beta)}{\cos (\alpha-\beta)} is equal to
View answer and explanation
Correct option: A
13\frac{1}{3}
Option A (13\frac{1}{3}) is correct because by using the given equation and applying the cosine addition and subtraction formulas, the expression simplifies to 13\frac{1}{3}.
88 Easy
88 of 147
Application +4 | -1
The value of tan⁡40∘+tan⁡20∘+3tan⁡20∘tan⁡40∘\tan 40^\circ + \tan 20^\circ + \sqrt 3 \tan 20^\circ \tan 40^\circ is equal to
View answer and explanation
Correct option: D
3\sqrt 3
Option D (3\sqrt{3}) is correct because by using the tangent addition formula, tan⁡(A+B)=tan⁡A+tan⁡B1−tan⁡Atan⁡B\tan(A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}, and rearranging the terms, we can show that the given expression is equal to tan⁡60∘=3\tan 60^\circ = \sqrt{3}.
89 Medium
89 of 147
Application +4 | -1
If cos⁡Acos⁡B=n\frac{{\cos A}}{{\cos B}} = n and sin⁡Asin⁡B=m\frac{{\sin A}}{{\sin B}} = m, then (m2−n2)sin⁡2B=\left( {{m^2} - {n^2}} \right){\sin ^2}B =
View answer and explanation
Correct option: A
1−n21 - {n^2}
Option A (1−n21 - {n^2}) is correct because it is derived by manipulating the given trigonometric ratios and applying trigonometric identities.
90 Medium
90 of 147
Application +4 | -1
If A+C=BA + C = B, then tan⁡A  tan⁡B  tan⁡C=\tan A\,\,\tan B\,\,\tan C =
View answer and explanation
Correct option: B
tan⁡  B−tan⁡  C−tan⁡  A\tan \,\,B - \tan \,\,C - \tan \,\,A
Option B (p2=q(q+2){p^2} = q\left( {q + 2} \right)) is correct because it is derived by using the relationship between roots and coefficients of a quadratic equation and trigonometric identities.
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