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JEE • MATHEMATICS • MULTIPLE AND SUBMULTIPLE ANGLES

Multiple and submultiple 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 1-30 of 122 questions
1 Easy
1 of 122
Application +4 | -1
If 1+cos⁡  x=k1 + \cos \,\,x = k, where xx is acute, then sin⁡  x2\sin \,\,\frac{x}{2} is
View answer and explanation
Correct option: D
2−k2\sqrt {\frac{{2 - k}}{2}}
Option D (2−k2\sqrt {\frac{{2 - k}}{2}}) is correct because by using the half-angle formula for sine and the given equation, we can derive this expression.
2 Medium
2 of 122
Application +4 | -1
The value of sin⁡12∘⋅sin⁡48∘⋅sin⁡54∘=\sin 12^\circ \cdot \sin 48^\circ \cdot \sin 54^\circ =
View answer and explanation
Correct option: A
1/81/8
Option A (1/8) is correct because by using the product-to-sum trigonometric identities, the expression simplifies to 1/8.
3 Medium
3 of 122
Application +4 | -1
If α,    β(α≠β)\alpha ,\;\,\,\beta \left( {\alpha \ne \beta } \right) satisfies the equation a a  cos⁡  θ+b  sin⁡  θ=ca\,\,\cos \,\,\theta + b\,\,\sin \,\,\theta = c, then the value of tan⁡  (α+β2)\tan \,\,\left( {\frac{{\alpha + \beta }}{2}} \right) is

View answer and explanation
Correct option: A
b/ab/a
Option A (b/a) is correct because by using trigonometric identities and subtracting the equations for α and β, we can derive the value of tan((α + β)/2).
4 Medium
4 of 122
Application +4 | -1
cos⁡4θ−sin⁡4θ{\cos ^4}\theta - {\sin ^4}\theta is equal to
View answer and explanation
Correct option: B
2  cos⁡2θ−12\,\,{\cos ^2}\theta - 1
Option B is correct because the expression simplifies to cos⁡2θ\cos 2\theta, which is equivalent to 2cos⁡2θ−12{\cos ^2}\theta - 1.
5 Medium
5 of 122
Analyzing +4 | -1
The value of
cos⁡210∘−cos⁡10∘cos⁡50∘+cos⁡250∘\cos ^{2} 10^{\circ}-\cos 10^{\circ} \cos 50^{\circ}+\cos ^{2} 50^{\circ} is :
View answer and explanation
Correct option: B
3/43 / 4
Option B (3/4) is correct because the trigonometric expression simplifies to 3/4 after applying trigonometric identities and simplifications.
6 Medium
6 of 122
Analyzing +4 | -1
In a △PQR,∠R=π2\triangle P Q R, \angle R=\frac{\pi}{2}. If tan⁡(P2)\tan \left(\frac{P}{2}\right) and tan⁡(Q2)\tan \left(\frac{Q}{2}\right) are the roots of ax2+bx+c=0,a≠0a x^2+b x+c=0, a \neq 0, then
View answer and explanation
Correct option: C
c=a+bc=a+b
Option C (c=a+bc=a+b) is correct because it is derived from the relationship between the tangent of half angles and the sum of angles in a right-angled triangle.
7 Medium
7 of 122
Application +4 | -1
If 0<α<π/60<\alpha<\pi / 6 and sin⁡α+cos⁡α=7/2\sin \alpha+\cos \alpha=\sqrt{7} / 2, then tan⁡α/2\tan \alpha / 2 is equal to
View answer and explanation
Correct option: A
7−23\frac{\sqrt{7}-2}{3}
Option A (7−23\frac{{\sqrt{{7}}-2}}{{3}}) is correct because solving the trigonometric equation and considering the given range for α\alpha, the value of tan⁡α2\tan \frac{{\alpha}}{{2}} is 7−23\frac{{\sqrt{{7}}-2}}{{3}}.
8 Medium
8 of 122
Analyzing +4 | -1
If tan⁡3Atan⁡A=k\frac{\tan ^3 A}{\tan A}=k, then sin⁡3Asin⁡A\frac{\sin 3 A}{\sin A} is equal to
View answer and explanation
Correct option: A
2kk−1\frac{2 k}{k-1}
Option A (2kk−1\frac{2 k}{k-1}) is correct because by using trigonometric identities and simplifying the given expression, we can find that sin⁡3Asin⁡A=2kk−1\frac{\sin 3 A}{\sin A} = \frac{2k}{k-1}.
9 Medium
9 of 122
Application +4 | -1
If cos⁡θa=sin⁡θb\frac{\cos \theta}{a}=\frac{\sin \theta}{b}, then asec⁡2θ+bcosec⁡2θ\frac{a}{\sec 2 \theta}+\frac{b}{\operatorname{cosec} 2 \theta} is equal to
View answer and explanation
Correct option: A
aa
Option A (aa) is correct because the expression simplifies to acos⁡2θ+bsin⁡2θ=aa \cos 2\theta + b \sin 2\theta = a.
10 Medium
10 of 122
Analyzing +4 | -1
If 5(tan⁡2x−cos⁡2x)=2cos⁡2x+95\left(\tan ^{2} x-\cos ^{2} x\right)=2 \cos 2 x+9, then the value of cos⁡4x\cos 4 x is
View answer and explanation
Correct option: A
−79-\frac{7}{9}
Option A (-7/9) is correct because after simplifying the given equation and solving for cos⁡2x\cos 2x, we can find cos⁡4x\cos 4x which equals -7/9.
11 Medium
11 of 122
Application +4 | -1
The value of tan⁡  821∘2\tan \,\,82\frac{{1^\circ }}{2}, is
View answer and explanation
Correct option: A
2+3+4+6\sqrt 2 + \sqrt 3 + \sqrt 4 + \sqrt 6
Option A (2+3+4+6\sqrt 2 + \sqrt 3 + \sqrt 4 + \sqrt 6) is the correct answer because it is obtained by simplifying the expression for tan⁡82.5∘\tan 82.5^\circ using trigonometric identities.
12 Easy
12 of 122
Application +4 | -1
If tan⁡  α=ba,   a>b>0\tan \,\,\alpha = \frac{b}{a},\,\;a > b > 0 and if 0<α<π40 < \alpha < \frac{\pi }{4}, then a+ba−b  −  a−ba+b\sqrt {\frac{{a + b}}{{a - b}}} \,\, - \,\,\sqrt {\frac{{a - b}}{{a + b}}} is equal to

View answer and explanation
Correct option: A
2  sin⁡  αcos⁡  2α\frac{{2\,\,\sin \,\,\alpha }}{{\sqrt {\cos \,\,2\alpha } }}
The correct answer is A (2sin⁡αcos⁡,2α\frac{{2\sin \alpha }}{{\sqrt {\cos \\,2\alpha } }}) because simplifying the given expression using trigonometric identities leads to this result.
13 Medium
13 of 122
Application +4 | -1
If sin⁡α=336625\sin \alpha=\frac{336}{625} and 450∘<α<540∘450^{\circ}<\alpha<540^{\circ}, then sin⁡(α/4)\sin (\alpha / 4) is equal to
View answer and explanation
Correct option: A
152\frac{1}{5 \sqrt{2}}
Option A (152\frac{{1}}{{5\sqrt{{2}}}}) is correct because by using the given information and applying trigonometric identities repeatedly, the value of sin⁡(α/4)\sin(\alpha/4) is found to be 152\frac{{1}}{{5\sqrt{{2}}}}.
14 Easy
14 of 122
Application +4 | -1
The value of

cos⁡π65cos⁡2π65cos⁡4π65cos⁡8π65cos⁡16π65cos⁡32π65\cos \frac{\pi}{65} \cos \frac{2 \pi}{65} \cos \frac{4 \pi}{65} \cos \frac{8 \pi}{65} \cos \frac{16 \pi}{65} \cos \frac{32 \pi}{65}
is equal to
View answer and explanation
Correct option: A
164\frac{1}{64}
Option A (164\frac{1}{64}) is correct because the given expression can be simplified using the double angle formula repeatedly.
15 Medium
15 of 122
Application +4 | -1
The value of (1+cos⁡  π6)  (1+cos⁡  π3)  (1+cos⁡  2π3)  (1+cos⁡  7π6)\left( {1 + \cos \,\,\frac{\pi }{6}} \right)\,\,\left( {1 + \cos \,\,\frac{\pi }{3}} \right)\,\,\left( {1 + \cos \,\,\frac{{2\pi }}{3}} \right)\,\,\left( {1 + \cos \,\,\frac{{7\pi }}{6}} \right) is
View answer and explanation
Correct option: A
316\frac{3}{{16}}
Option A (316\frac{3}{{16}}) is correct because it is derived by substituting the values of the cosine function and simplifying the expression.

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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
16 Easy
16 of 122
Application +4 | -1
The value of   cos⁡  π65  cos⁡  2 π65  cos  4 π65  …  cos⁡  32 π65\mathrm{\;}\cos \,\,\frac{\mathrm{\pi }}{{65}}\,\,\cos \,\,\frac{{2\,\mathrm{\pi }}}{{65}}\,\,\mathrm{cos}\,\,\frac{{4\,\mathrm{\pi }}}{{65}}\,\, \ldots \,\,\cos \,\,\frac{{32\,\mathrm{\pi }}}{{65}} is
View answer and explanation
Correct option: B
164\frac{1}{{64}}
Option B (164\frac{1}{{64}}) is correct because repeated application of the identity sin⁡2x=2sin⁡xcos⁡x\sin 2x = 2 \sin x \cos x simplifies the expression.
17 Easy
17 of 122
Analyzing +4 | -1
If   α,  β,  γ, δ\;\alpha ,\,\,\beta ,\,\,\gamma ,\,\delta are four solutions of the equation tan⁡  (θ+π4)=3  tan⁡ 3θ\tan \,\,\left( {\mathrm{\theta } + \frac{\pi }{4}} \right) = 3\,\,\tan \,3\mathrm{\theta }, then
tan⁡  α  tan⁡  β  tan⁡  γ  tan⁡  δ  \tan \,\,\alpha \,\,\tan \,\,\beta \,\,\tan \,\,\gamma \,\,\tan \,\,\delta \; equals
View answer and explanation
Correct option: C
−13- \frac{1}{3}
Option C (−13\frac{{ - 1}}{3}) is correct because the product of the roots of the quartic equation formed from the given trigonometric equation is equal to −13\frac{{ - 1}}{3}.
18 Easy
18 of 122
Application +4 | -1
Simplest form of 22+2+2+2  cos⁡  4x\frac{2}{{\sqrt {2 + \sqrt {2 + \sqrt {2 + 2\,\,\cos \,\,4x} } } }} is
View answer and explanation
Correct option: A
sec⁡  x2\sec \,\,\frac{x}{2}
Option A (sec⁡  x2\sec \,\,\frac{x}{2}) is correct because it is obtained by repeatedly using the identity 2cos⁡2θ=1+cos⁡2θ2\cos^2 \theta = 1 + \cos 2\theta and simplifying the expression.
19 Medium
19 of 122
Application +4 | -1
If sin⁡α=336625\sin \alpha=\frac{336}{625} and 450∘<α<540∘450^{\circ} < \alpha < 540^{\circ}, then sin⁡(α/4)\sin (\alpha / 4) is equal to
View answer and explanation
Correct option: A
152\frac{1}{5 \sqrt{2}}
Option A (152\frac{1}{5 \sqrt{2}}) is correct because by using the given information and trigonometric identities, we can find the value of sin⁡(α/4)\sin(\alpha / 4).
20 Easy
20 of 122
Application +4 | -1
If tan⁡2θ=2tan⁡2ϕ+1,{\tan ^2}\theta = 2{\tan ^2}\phi + 1, then cos⁡2θ+sin⁡2ϕ\cos 2\theta + {\sin ^2}\phi is equal to
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the expression cos⁡2θ+sin⁡2ϕ\cos 2\theta + \sin^2 \phi simplifies to 0, which is not among the given options.
21 Easy
21 of 122
Application +4 | -1
tan⁡6  π9−33  tan⁡4  π9+27  tan⁡2  π9={\tan ^6}\,\,\frac{\pi }{9} - 33\,\,{\tan ^4}\,\,\frac{\pi }{9} + 27\,\,{\tan ^2}\,\,\frac{\pi }{9} =
View answer and explanation
Correct option: C
3
Option C (3) is correct because by using the triple angle formula for tangent, the expression simplifies to 3.
22 Medium
22 of 122
Analyzing +4 | -1
If θ=π/7\theta=\pi / 7, then cos⁡θ+cos⁡3θ+cos⁡5θ\cos \theta+\cos 3 \theta+\cos 5 \theta is
View answer and explanation
Correct option: A
12\frac{1}{2}
Option A (12\frac{1}{2}) is correct because the sum of the cosines can be simplified to 12\frac{1}{2} when θ=π7\theta = \frac{\pi}{7}.
23 Easy
23 of 122
Application +4 | -1
If   tan  α/2   and tan⁡β/2    \mathrm{\;tan}\,\,\alpha /2\,\;\mathrm{and}\,\tan \beta /2\;\; are the roots of the equation 8 x2−  26 x+15=08\,{x^2} - \;26\,x + 15 = 0 then
cos⁡ (α+β)\cos \,\left( {\alpha + \beta } \right) is equal to
View answer and explanation
Correct option: A
−627725- \frac{{627}}{{725}}
Option A is correct because by finding the sum and product of the roots of the quadratic equation, we can determine \tan \left( {\frac{{\alpha + \mathrm{\beta }}}}{2} \right)\tan \left( {\frac{{\alpha + \mathrm{\beta }}}}{2} \right) and then calculate cos⁡(α+β)\cos \left( {\alpha + \mathrm{\beta }} \right) using trigonometric identities.
24 Easy
24 of 122
Application +4 | -1
The value of cot⁡x−tan⁡xcot⁡  2x\frac{{\cot x - \tan x}}{{\cot \,\,2x}} is
View answer and explanation
Correct option: B
2
Option B (2) is correct because simplifying the given trigonometric expression using identities leads to the value 2.
25 Medium
25 of 122
Application +4 | -1
If tan⁡  x=ba\tan \,\,x = \frac{b}{a}, then the value of a  cos⁡  2x+  b  sin⁡  2xa\,\,\cos \,\,2x + \,\,b\,\,\sin \,\,2x is
View answer and explanation
Correct option: D
aa
Option D is correct because by substituting the value of tan x and simplifying, the expression reduces to 'a'.
26 Medium
26 of 122
Analyzing +4 | -1
The value of cos⁡π11cos⁡2π11cos⁡3π11………cos⁡11π11\cos \frac{\pi}{11} \cos \frac{2 \pi}{11} \cos \frac{3 \pi}{11} \ldots \ldots \ldots \cos \frac{11 \pi}{11} is equal to
View answer and explanation
Correct option: C
11024\frac{1}{{1024}}
Option C (11024\frac{1}{{1024}}) is correct because the product can be simplified using trigonometric identities and the sine product formula.
27 Medium
27 of 122
Analyzing +4 | -1
The expression cos⁡2(A−B)+cos⁡2B−2  cos⁡(A−B)cos⁡A  cos⁡B  {\cos ^2}\left( {A - B} \right) + {\cos ^2}B - 2\,\,\cos \left( {A - B} \right)\cos A\,\,\cos B\; is
View answer and explanation
Correct option: C
dependent on AA
Option C (dependent on AA) is correct because the expression simplifies to sin⁡2A{\sin ^2}A, which depends only on AA.
28 Medium
28 of 122
Application +4 | -1
θ\theta and ϕ\phi are acute angles. If sin⁡θ=12\sin \theta=\frac{1}{2} and cos⁡ϕ=13\cos \phi=\frac{1}{3}, then θ+ϕ∈…\theta+\phi \in \ldots.
View answer and explanation
Correct option: B
(π2,2π3)\left(\frac{\pi}{2}, \frac{2 \pi}{3}\right)
Option B ((π2,2π3)\left(\frac{{\pi}}{{2}}, \frac{{2 \pi}}{{3}}\right)) is correct because given the values of sin⁡θ\sin \theta and cos⁡ϕ\cos \phi, the sum θ+ϕ\theta + \phi falls within this interval.
29 Easy
29 of 122
Application +4 | -1
1−tan⁡2  (45∘−A)1+tan⁡2  (45∘−A)\frac{{1 - {{\tan }^2}\,\,\left( {45^\circ - A} \right)}}{{1 + {{\tan }^2}\,\,\left( {45^\circ - A} \right)}} is equal to
View answer and explanation
Correct option: A
sin⁡  2A\sin \,\,2A
Option B (ab\frac{a}{b}) is correct because by applying the componendo and dividendo rule and trigonometric identities, the expression simplifies to ab\frac{a}{b}.
30 Easy
30 of 122
Application +4 | -1
If x+1x=2  cos⁡  θx + \frac{1}{x} = 2\,\,\cos \,\,\theta, then xn+1xn{x^n} + \frac{1}{{{x^n}}} is equal to
View answer and explanation
Correct option: B
2  cos⁡  nθ2\,\,\cos \,\,n\theta
Option B (2 cos⁡ nθ2\,\cos \,n\theta) is correct because if x+1x=2 cos⁡θx + \frac{1}{x} = 2\,\cos \theta, then xn+1xn=2 cos⁡ nθ{x^n} + \frac{1}{{{x^n}}} = 2\,\cos \,n\theta.
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Key Takeaways

  • ✓ This set contains 122 single-correct-answer MCQs on MULTIPLE AND SUBMULTIPLE ANGLES.
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