Skip to main content
Back to MULTIPLE AND SUBMULTIPLE ANGLES

Your Progress

0 / 66 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • MULTIPLE AND SUBMULTIPLE ANGLES

Multiple and submultiple angles practice · Easy

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

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.

Take a chapter quiz →
Showing 31-60 of 66 questions
31 Easy
31 of 66
Application +4 | -1
The value of tan⁡  67  1∘2+cot⁡  67  1∘2\tan \,\,67\,\,\frac{{1^\circ }}{2} + \cot \,\,67\,\,\frac{{1^\circ }}{2} is
View answer and explanation
Correct option: C
2 22\,\sqrt 2
Option C (222\sqrt 2) is correct because simplifying the expression using trigonometric identities leads to the result 222\sqrt 2.
32 Easy
32 of 66
Application +4 | -1
If   x  cos⁡  θ=y  cos⁡(θ+2π3)=z  cos⁡(θ+4π3)  \;x\,\,\cos \,\,\mathrm{\theta } = y\,\,\cos \left( {\mathrm{\theta } + \frac{{2\pi }}{3}} \right) = \mathrm{z}\,\,\cos \left( {\mathrm{\theta } + \frac{{4\pi }}{3}} \right)\;, then the value of 1x+1y+1z\frac{1}{x} + \frac{1}{y} + \frac{1}{\mathrm{z}} is equal to
View answer and explanation
Correct option: C
0
Option C (0) is correct because the sum of the cosines with the given phase shifts equals zero, leading to the result 1/x + 1/y + 1/z = 0.
33 Easy
33 of 66
Application +4 | -1
If cosec    θ=p+qp−q\mathrm{cosec}\;\,\,\theta = \frac{{p + q}}{{p - q}}, then cot⁡  (π/4+θ/2)=\cot \,\,\left( {\pi /4 + \theta /2} \right) =
View answer and explanation
Correct option: B
qp\sqrt {\frac{q}{p}}
Option B, qp\sqrt {\frac{q}{p}}, is correct because it is the simplified form of cot⁡(π/4+θ/2)\cot \left( {\pi /4 + \theta /2} \right) after substituting the given value of cosec   θ\mathrm{cosec}\;\,\theta and using trigonometric identities.
34 Easy
34 of 66
Application +4 | -1
The value of the series

cos⁡  12∘+cos⁡  84∘+cos⁡  132∘+cos⁡  156∘\cos \,\,12^\circ + \cos \,\,84^\circ + \cos \,\,132^\circ + \cos \,\,156^\circ is
View answer and explanation
Correct option: D
−12- \frac{1}{2}
Option D is correct because the sum of the cosine series simplifies to -1/2 using trigonometric identities.
35 Easy
35 of 66
Application +4 | -1
The value of     (1+cos  π8)  (1+cos  3π8)  (1+cos  5π8)  (1+cos  7π8)  \mathrm{\;\;}\left( {1 + \mathrm{cos}\,\,\frac{\mathrm{\pi }}{8}} \right)\,\,\left( {1 + \mathrm{cos}\,\,\frac{{3\mathrm{\pi }}}{8}} \right)\,\,\left( {1 + \mathrm{cos}\,\,\frac{{5\mathrm{\pi }}}{8}} \right)\,\,\left( {1 + \mathrm{cos}\,\,\frac{{7\mathrm{\pi }}}{8}} \right)\mathrm{\;} is equal to
View answer and explanation
Correct option: C
18\frac{1}{8}
Option D (nπ+π4n\pi \\ + \\ \frac{\pi }{4}) is correct because by simplifying the equation, we get tan⁡θ=1\tan \theta = 1, which gives the general solution θ=nπ+π4\theta = n\pi + \frac{\pi}{4}.
36 Easy
36 of 66
Application +4 | -1
The value of
cos⁡2  π16+cos⁡2  3π16+cos⁡2  5π16+cos⁡2  7π16{\cos ^2}\,\,\frac{\pi }{{16}} + {\cos ^2}\,\,\frac{{3\pi }}{{16}} + {\cos ^2}\,\,\frac{{5\pi }}{{16}} + {\cos ^2}\,\,\frac{{7\pi }}{{16}}
View answer and explanation
Correct option: A
2
Option A (2) is correct because using trigonometric identities, the expression simplifies to 2.
37 Easy
37 of 66
Analyzing +4 | -1
(1+cos⁡  π8)  (1+cos⁡  3 π8)  (1+cos⁡  5 π8)  (1+cos⁡  7π8)\left( {1 + \cos \,\,\frac{\pi }{8}} \right)\,\,\left( {1 + \cos \,\,\frac{{3\,\pi }}{8}} \right)\,\,\left( {1 + \cos \,\,\frac{{5\,\pi }}{8}} \right)\,\,\left( {1 + \cos \,\,\frac{{7\pi }}{8}} \right) is equal to
View answer and explanation
Correct option: C
18\frac{1}{8}
Option C (18\frac{1}{8}) is correct because the given expression simplifies to 18\frac{1}{8} using trigonometric identities and properties of cosine.
38 Easy
38 of 66
Application +4 | -1
If tan⁡x=ba\tan x=\frac{b}{a}, then a+ba−b+a−ba+b=\sqrt{\frac{a+b}{a-b}}+\sqrt{\frac{a-b}{a+b}}=
View answer and explanation
Correct option: B
2cos⁡xcos⁡2x\frac{2 \cos x}{\sqrt{\cos 2 x}}
Option B (2cos⁡xcos⁡2x\frac{{2 \cos x}}{{\sqrt{{\cos 2 x}}}}) is correct because, after using componendo and dividendo and simplifying, the expression equals 2cos⁡xcos⁡2x\frac{{2 \cos x}}{{\sqrt{{\cos 2 x}}}}.
39 Easy
39 of 66
Application +4 | -1
The value of   tan  20∘  tan⁡  40∘  tan⁡  60∘  tan⁡  80∘  \mathrm{\;tan}\,\,20^\circ \,\,\tan \,\,40^\circ \,\,\tan \,\,60^\circ \,\,\tan \,\,80^\circ \mathrm{\;} is equal to
View answer and explanation
Correct option: C
3
Option C (3) is correct because the product of the tangent values simplifies to 3 using trigonometric identities.
40 Easy
40 of 66
Analyzing +4 | -1
If tan⁡  x=2ba−c,   a≠c\tan \,\,x = \frac{{2b}}{{a - c}},\,\;a \ne c and y=a  cos⁡2 x  +  2b  sin⁡  x  cos⁡  x  +  c  sin⁡2 xy = a\,\,{\cos ^2}\,x\,\, + \,\,2b\,\,\sin \,\,x\,\,\cos \,\,x\,\, + \,\,c\,\,{\sin ^2}\,x

z=a  sin⁡2 x  −  2b  sin⁡  x  cos⁡  x  +  c  cos⁡2 xz = a\,\,{\sin ^2}\,x\,\, - \,\,2b\,\,\sin \,\,x\,\,\cos \,\,x\,\, + \,\,c\,\,{\cos ^2}\,x, then
View answer and explanation
Correct option: C
y−z=a−cy - z = a - c
Option C (y−z=a−cy - z = a - c) is correct because simplifying the expression y−zy - z using trigonometric identities and the given condition tan⁡x=2ba−c\tan x = \frac{{2b}}{{a - c}} leads to the result a−ca - c.
41 Easy
41 of 66
Understanding +4 | -1
1+cos⁡22A1+\cos ^2 2 A is equal to
View answer and explanation
Correct option: C
2(cos⁡4 A+sin⁡4 A)2\left(\cos ^4 \mathrm{~A}+\sin ^4 \mathrm{~A}\right)
Option C (2(cos⁡4A+sin⁡4A)2(\cos ^4 A+\sin ^4 A)) is correct because it is the simplified form of the given expression using trigonometric identities.
42 Easy
42 of 66
Application +4 | -1
If cos⁡A=3/4\cos A=3 / 4 then value of 32sin⁡(A/2)sin⁡(5 A/2)32 \sin (A / 2) \sin (5 \mathrm{~A} / 2) is equal to
View answer and explanation
Correct option: C
11
Option C (11) is correct because it is the result of applying the product-to-sum trigonometric identity and simplifying using the given value of cos⁡A\cos A.
43 Easy
43 of 66
Application +4 | -1
If sin    (x+y)sin⁡    (x−y)=a+ba−b\frac{{\mathrm{sin}\,\,\mathrm{\;}\left( {x + y} \right)}}{{\sin \,\,\;\left( {x - y} \right)}} = \frac{{a + b}}{{a - b}}, then tan⁡  xtan⁡  y\frac{{\tan \,\,x}}{{\tan \,\,y}} is equal to
View answer and explanation
Correct option: B
ab\frac{a}{b}
Option B (ab\frac{a}{b}) is correct because by applying the componendo and dividendo rule and trigonometric identities, the ratio of tangents simplifies to ab\frac{a}{b}.
44 Easy
44 of 66
Application +4 | -1
If 5cos⁡  2θ+2cos⁡2θ2+1=0,  −π<θ<π5\cos \,\,2\theta + 2{\cos ^2}\frac{\theta }{2} + 1 = 0,\; - \pi < \theta < \pi, then θ\theta is equal to

View answer and explanation
Correct option: D
π3,   π−cos⁡−1(35)\frac{\pi }{3},\;\,\pi - {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)
Option D (π3,   π−cos⁡−1(35)\frac{\pi }{3},\;\,\pi - {\cos ^{ - 1}}\left( {\frac{3}{5}} \right)) is correct because it represents the solutions obtained by solving the given trigonometric equation within the specified interval.
45 Easy
45 of 66
Analyzing +4 | -1
If 2  cos⁡  A2=1+sin⁡  A+1−sin⁡  A2\,\,\cos \,\,\frac{A}{2} = \sqrt {1 + \sin \,\,A} + \sqrt {1 - \sin \,\,A}, then A2\frac{A}{2} lies between, (n∈Z)\left( {n \in Z} \right)
View answer and explanation
Correct option: B
2n  π−π42n\;\pi - \frac{\pi }{4} and 2n  π+π42n\;\pi + \frac{\pi }{4}
Option C (cot⁡B\cot B) is correct because simplifying the given expression using trigonometric identities leads to this result.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
46 Easy
46 of 66
Application +4 | -1
The value of 2+2+2+2cos⁡8θ\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}}, where 0<θ<π80 < \theta < \frac{\pi}{8}, is
View answer and explanation
Correct option: A
2cos⁡θ2 \cos \theta
Option A (2cos⁡θ2 \cos \theta) is correct because the nested square roots simplify to 2cos⁡θ2 \cos \theta using the double angle formula for cosine.
47 Easy
47 of 66
Application +4 | -1
The value of cos⁡  π15  cos⁡  2 π15  cos⁡  3 π15  cos⁡  4 π15  cos⁡  5 π15  cos⁡  6 π15  cos⁡  7π15\cos \,\,\frac{\pi }{{15}}\,\,\cos \,\,\frac{{2\,\pi }}{{15}}\,\,\cos \,\,\frac{{3\,\pi }}{{15}}\,\,\cos \,\,\frac{{4\,\pi }}{{15}}\,\,\cos \,\,\frac{{5\,\pi }}{{15}}\,\,\cos \,\,\frac{{6\,\pi }}{{15}}\,\,\cos \,\,\frac{{7\pi }}{{15}}, is
View answer and explanation
Correct option: A
1/1281/128
Option A (1/1281/128) is correct because the expression can be simplified using the identity ∏k=1n−1cos⁡(kπ2n)=n2n−1\prod_{k=1}^{n-1} \cos(\frac{k\pi}{2n}) = \frac{\sqrt{n}}{2^{n-1}}.
48 Easy
48 of 66
Application +4 | -1
If cos⁡  (θ−α),  cos⁡  θ,  cos⁡  (θ+α)\cos \,\,\left( {\theta - \alpha } \right),\,\,\cos \,\,\theta ,\,\,\cos \,\,\left( {\theta + \alpha } \right) are in H.P., then cos⁡  θ  sec⁡  (α2)\cos \,\,\theta \,\,\sec \,\,\left( {\frac{\alpha }{2}} \right) is equal to
View answer and explanation
Correct option: B
±   2\pm \;\,\sqrt 2
Option B (±   2\pm \;\,\sqrt 2) is correct because by using the harmonic progression property and trigonometric identities, the expression cos⁡ θ  sec⁡ (α2)\cos \,\theta \,\,\sec \,\left( {\frac{\alpha }{2}} \right) simplifies to ±   2\pm \;\,\sqrt 2.
49 Easy
49 of 66
Analyzing +4 | -1
If sin⁡x+sin⁡y=3(cos⁡y−cos⁡x)\sin x + \sin y = 3\left( {\cos y - \cos x} \right), then the value of sin⁡3xsin⁡3y\frac{{\sin 3x}}{{\sin 3y}} is
View answer and explanation
Correct option: B
−1- 1
Option B (-1) is correct because by simplifying the given equation, we find a relationship between x and y, allowing us to evaluate the expression.
50 Easy
50 of 66
Analyzing +4 | -1
The value of sin⁡  15 π32  sin⁡  7π16  sin⁡  3 π8\sin \,\,\frac{{15\,\pi }}{{32}}\,\,\sin \,\,\frac{{7\pi }}{{16}}\,\,\sin \,\,\frac{{3\,\pi }}{8} is
View answer and explanation
Correct option: A
18 2  cos⁡  (15π32)\frac{1}{{8\,\sqrt 2 \,\,\cos \,\,\left( {\frac{{15\pi }}{{32}}} \right)}}
Option A (182cos⁡(15π32)\frac{1}{{8\sqrt 2 \cos \left( {\frac{{15\pi }}{{32}}} \right)}}) is correct because it is derived by repeatedly applying the double angle formula for sine.
51 Easy
51 of 66
Analyzing +4 | -1
tan⁡  α+2  tan⁡  2α+4  tan⁡  4α+8  cot⁡  8α\tan \,\,\alpha + 2\,\,\tan \,\,2\alpha + 4\,\,\tan \,\,4\alpha + 8\,\,\cot \,\,8\alpha is equal to
View answer and explanation
Correct option: C
cot⁡  α\cot \,\,\alpha
Option C (cot⁡α\cot \alpha) is correct because the given expression simplifies to cot⁡α\cot \alpha using the identity cot⁡2x=cot⁡x−tan⁡x2\cot 2x = \frac{{\cot x - \tan x}}{2}.
52 Easy
52 of 66
Application +4 | -1
Suppose 0<t<π0 < t < \pi and sin⁡  t+cos⁡  t=15\sin \,\,t + \cos \,\,t = \frac{1}{5}. Then, tan⁡  t2\tan \,\,\frac{t}{2} is equal to
View answer and explanation
Correct option: A
2
Option A, 2, is correct because it is the value of tan⁡t2\tan \frac{t}{2} obtained by substituting the given expression into the trigonometric identity and solving the resulting quadratic equation.
53 Easy
53 of 66
Application +4 | -1
sin⁡4  π8+sin⁡4  3 π8+sin⁡4  5 π8+sin⁡4  7π8  {\sin ^4}\,\,\frac{\pi }{8} + {\sin ^4}\,\,\frac{{3\,\pi }}{8} + {\sin ^4}\,\,\frac{{5\,\pi }}{8} + {\sin ^4}\,\,\frac{{7\pi }}{8}\; is equal to
View answer and explanation
Correct option: B
3 / 2\mathrm{3}\,\mathrm{/}\,\mathrm{2}
Option B (3/2) is correct because the given trigonometric expression simplifies to 3/2 using trigonometric identities and properties.
54 Easy
54 of 66
Application +4 | -1
The value of cos⁡π22⋅cos⁡π23.......cos⁡π210⋅sin⁡π210\cos \frac{\pi }{{{2^2}}} \cdot \cos \frac{\pi }{{{2^3}}}.......\cos \frac{\pi }{{{2^{10}}}} \cdot \sin \frac{\pi }{{{2^{10}}}} is
View answer and explanation
Correct option: C
1512\frac{1}{{512}}
Option C (1512\frac{1}{{512}}) is correct because it is the simplified result after applying the trigonometric identity for the product of cosines and sine.
55 Easy
55 of 66
Application +4 | -1
If cos⁡  (x−y),  cos⁡x\cos \,\,\left( {x - y} \right),\,\,\cos x and cos⁡  (x+y)\cos \,\,\left( {x + y} \right) are in H.P., then ∣ cos⁡x  sec⁡  y2 ∣\left| {\,\cos x\,\,\sec \,\,\frac{y}{2}\,} \right| equals
View answer and explanation
Correct option: C
2\sqrt 2
Option C (2\sqrt 2) is correct because after applying the properties of Harmonic Progression and trigonometric identities, the expression simplifies to 2\sqrt{2}.
56 Easy
56 of 66
Analyzing +4 | -1
sin⁡23 Asin⁡2 A−cos⁡23 Acos⁡2A=\frac{{{{\sin }^2}3\,A}}{{{{\sin }^2}\,A}} - \frac{{{{\cos }^2}3\,A}}{{{{\cos }^2}A}} =
View answer and explanation
Correct option: B
8  cos⁡  2A8\;\cos \,\,2A
Option B (8  cos⁡  2A8\;\cos \;2A) is correct because the expression simplifies to 8cos⁡2A8\cos 2A using trigonometric identities.
57 Easy
57 of 66
Application +4 | -1
If sin⁡A=336625\sin A = \frac{{336}}{{625}} where 450∘  <A<540∘450^\circ \,\, < A < 540^\circ, then sin⁡  A4=\sin \,\,\frac{A}{4} =
View answer and explanation
Correct option: C
45\frac{4}{5}
Option C (45\frac{4}{5}) is correct because given the range of A and the value of sin⁡A\sin A, we can find sin⁡A4\sin \frac{A}{4} using half-angle formulas.
58 Easy
58 of 66
Analyzing +4 | -1
If cos⁡  x=tan⁡y,  cos⁡  y=tan⁡  z,  cos⁡  z=tan⁡ x\cos \,\,x = \tan y,\,\,\cos \,\,y = \tan \,\,z,\,\,\cos \,\,z = \tan \,x, then the value of sin⁡x\sin x is
View answer and explanation
Correct option: D
2sin⁡ 18∘2\sin \,18^\circ
Option D (2sin⁡ 18∘2\sin \,18^\circ) is the correct answer because, after simplification and solving the trigonometric equations, the value of sin⁡x\sin x is found to be equal to 2sin⁡ 18∘2\sin \,18^\circ.
59 Easy
59 of 66
Application +4 | -1
2sin⁡(π22)sin⁡(3π22)sin⁡(5π22)sin⁡(7π22)sin⁡(9π22)2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right) is equal to:
View answer and explanation
Correct option: B
116\frac{1}{{16}}
Option B (5) is correct because setting up the integral for the area and solving for 'a' yields the odd natural number 5.
60 Easy
60 of 66
Application +4 | -1
The value of sin⁡  36∘  sin⁡  72∘  sin⁡  108∘  sin⁡144∘\sin \,\,36^\circ \,\,\sin \,\,72^\circ \,\,\sin \,\,108^\circ \,\,\sin 144^\circ is
View answer and explanation
Correct option: D
516\frac{5}{{16}}
Option D (5/16) is correct because it is the result of simplifying the given expression using trigonometric identities and known values of sine functions.
Revision notes and key takeaways

Review MULTIPLE AND SUBMULTIPLE ANGLES in your textbook or class notes, then use this set to check your understanding.

Showing 31-60 of 66 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - MULTIPLE AND SUBMULTIPLE ANGLES MCQs (All) 122 MCQs → ENGINEERING MATHEMATICS - MULTIPLE AND SUBMULTIPLE ANGLES MCQs (Hard) 4 MCQs → ENGINEERING MATHEMATICS - MULTIPLE AND SUBMULTIPLE ANGLES MCQs (Medium) 52 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs
📚 Switch Set (EASY)
Chapter Sets
ALL 122 MCQs EASY 66 MCQs HARD 4 MCQs MEDIUM 52 MCQs
0 /66
0✓ 0✗
0% Accuracy
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →