Skip to main content
Back to COMPOUND ANGLES

Your Progress

0 / 91 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • COMPOUND ANGLES

Compound angles practice · Easy

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

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 61-90 of 91 questions

Preparing practice and saved progress…

61 Easy
61 of 91
Application +4 | -1
The value of   sin⁡  A  sin⁡(60∘−A)  sin⁡  (60∘+A)\mathrm{\;}\sin \,\,A\,\,\sin \left( {60^\circ - A} \right)\,\,\sin \,\,\left( {60^\circ + A} \right) is equal to
View answer and explanation
Correct option: C
sin⁡  3A4\frac{{\sin \,\,3A}}{4}
Option C (sin⁡ 3A4\frac{{\sin \,3A}}{4}) is correct because it is the result of applying the product-to-sum trigonometric identities.
62 Easy
62 of 91
Analyzing +4 | -1
In a △ABC\triangle A B C, if aa is the arithmetic mean and b,cb, c are two geometric means between any two positive number. Then, sin⁡3B+sin⁡3Csin⁡Asin⁡Bsin⁡C\frac{\sin ^3 B+\sin ^3 C}{\sin A \sin B \sin C} is equal to
View answer and explanation
Correct option: A
2
Option A (2) is correct because after substituting the given conditions and simplifying, the expression equals 2.
63 Easy
63 of 91
Application +4 | -1
The numerical value of tan⁡20∘tan⁡80∘cot⁡50∘\tan 20^{\circ} \tan 80^{\circ} \cot 50^{\circ} is
View answer and explanation
Correct option: A
3\sqrt{3}
Option A (3\sqrt{{3}}) is correct because the expression simplifies to 3\sqrt{{3}} using trigonometric identities.
64 Easy
64 of 91
Application +4 | -1
tan⁡  2π5−  tan⁡  π15−3tan⁡  2π5  tan⁡  π15\tan \,\,\frac{{2\pi }}{5} - \,\,\tan \,\,\frac{\pi }{{15}} - \sqrt 3 \tan \,\,\frac{{2\pi }}{5}\,\,\tan \,\,\frac{\pi }{{15}} is equal to
View answer and explanation
Correct option: D
3\sqrt 3
Option D (3\sqrt 3) is correct because the expression simplifies to tan⁡(2π5−π15)=tan⁡(π3)=3\tan(\frac{{2\pi }}{5} - \frac{\pi }{{15}}) = \tan(\frac{\pi}{3}) = \sqrt{3} using the tangent subtraction formula.
65 Easy
65 of 91
Application +4 | -1
If sin⁡  x+cos⁡  x=15\sin \,\,x + \cos \,\,x = \frac{1}{5}, then tan⁡  2x\tan \,\,2x is
View answer and explanation
Correct option: B
247\frac{{24}}{{7}}
Option B (247\frac{{24}}{{7}}) is correct because by squaring the given equation and using trigonometric identities, we can find sin⁡2x\sin 2x and cos⁡2x\cos 2x, and then calculate tan⁡2x\tan 2x.
66 Easy
66 of 91
Application +4 | -1
If 0<α,β,γ<π/20<\alpha, \beta, \gamma<\pi / 2 such that α+β+γ=π2\alpha+\beta+\gamma=\frac{\pi}{2} and cot⁡α,cot⁡β,cot⁡\cot \alpha, \cot \beta, \cot γ\gamma are in arithmetic progression, then the value of cot⁡αcot⁡γ\cot \alpha \cot \gamma is
View answer and explanation
Correct option: B
3
The correct answer is A (n+m+1Cn+1{ }^{n+m+1} \mathrm{C}_{n+1}) because it is the result of applying the Hockey Stick Identity to the given summation.
67 Easy
67 of 91
Application +4 | -1
If cos⁡  α+cos⁡  β=0=sin⁡  α+sin⁡  β\cos \,\,\alpha + \cos \,\,\beta = 0 = \sin \,\,\alpha + \sin \,\,\beta, then cos⁡  2  α+cos⁡  2  β=\cos \,\,2\;\alpha + \cos \,\,2\;\beta =
View answer and explanation
Correct option: B
− 2  cos⁡  (α+β)- \,2\,\,\cos \,\,\left( {\alpha + \beta } \right)
Option B (−2cos⁡(α+β)-2 \cos(\alpha + \beta)) is correct because it is derived by squaring the given equations and using trigonometric identities.
68 Easy
68 of 91
Application +4 | -1
If α\alpha and β\beta satisfying 2  sec⁡  2α=tan⁡  β+cot⁡  β2\,\,\sec \,\,2\alpha = \tan \,\,\beta + \cot \,\,\beta, then α+β\alpha + \beta is equal to
View answer and explanation
Correct option: C
π4\frac{\pi }{4}
Option C (π4\frac{\pi}{4}) is correct because it is the value of α+β\alpha + \beta that satisfies the given trigonometric equation.
69 Easy
69 of 91
Application +4 | -1
If tan⁡15∘+1tan⁡75∘+1tan⁡105∘+tan⁡195∘=2a\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2 a, then the value of (a+1a)\left(a+\frac{1}{a}\right) is
View answer and explanation
Correct option: A
4
Option A (4) is correct because simplifying the trigonometric expression results in 2*tan(15), which leads to a = 2-sqrt(3), and a + 1/a = 4.
70 Easy
70 of 91
Application +4 | -1
cos⁡  α  sin⁡  (β−γ)+cos⁡  β  sin⁡  (γ−α)+cos⁡  γ  sin⁡  (α−β)\cos \,\,\alpha \,\,\sin \,\,\left( {\beta - \gamma } \right) + \cos \,\,\beta \,\,\sin \,\,\left( {\gamma - \alpha } \right) + \cos \,\,\gamma \,\,\sin \,\,\left( {\alpha - \beta } \right) is equal to
View answer and explanation
Correct option: A
0\mathrm{0}
Option A (0) is correct because the given trigonometric expression simplifies to zero using trigonometric identities.
71 Easy
71 of 91
Application +4 | -1
If     π2<α<π,  π<β<  3π2;  sin⁡  α=1517    and  tan⁡  β=125\;\;\frac{\pi }{2} < \alpha < \pi ,\,\,\pi < \beta < \,\,\frac{{3\pi }}{2};\,\,\sin \,\,\alpha = \frac{{15}}{{17}}\,\,\;\mathrm{and}\,\,\tan \,\,\beta = \frac{{12}}{5} then the value of sin⁡ (β−α)\sin \,\left( {\beta - \alpha } \right) is
View answer and explanation
Correct option: D
171221\frac{{171}}{{221}}
Option D (171221\frac{{171}}{{221}}) is correct because, by using the given trigonometric values and the angle subtraction formula, we can calculate the value of sin⁡(β−α)\sin(\beta - \alpha).
72 Easy
72 of 91
Application +4 | -1
If   tan⁡A−tan⁡  B=x   and  cot⁡  B−cot⁡  A=y,  then  cot⁡(A−B)\;\tan A - \tan \,\,B = x\,\mathrm{\;and}\,\,\cot \,\,B - \cot \,\,A = y,\mathrm{\;then}\,\,\cot \left( {A - B} \right) is equal to

View answer and explanation
Correct option: D
1x+1y\frac{1}{x} + \frac{1}{y}
Option D (1x+1y\frac{1}{x} + \frac{1}{y}) is correct because it represents the correct expression for cot⁡(A−B)\cot(A - B) in terms of xx and yy.
73 Easy
73 of 91
Application +4 | -1
If sin⁡  A=110    \sin \,\,A = \frac{1}{{\sqrt {10\;} }}\; and sin⁡  B=15  \sin \,\,B = \frac{1}{{\sqrt 5 \;}}, where A  A\; and B  B\; are positive acute angles, then (A+B )(A + B\,) is equal to
View answer and explanation
Correct option: D
π4\frac{\pi }{4}
Option D (π4\frac{\pi }{4}) is correct because the sum of angles A and B is calculated to be π4\frac{\pi }{4} using trigonometric identities.
74 Easy
74 of 91
Application +4 | -1
If cos⁡  (α+β)=45,  sin⁡  (α−β)=513\cos \,\,\left( {\alpha + \beta } \right) = \frac{4}{5},\,\,\sin \,\,\left( {\alpha - \beta } \right) = \frac{5}{{13}} and α,   β\alpha ,\;\,\beta lie between 0\mathrm{0} and π4\frac{\pi }{4}, then tan⁡  2α=\tan \,\,2\alpha =

View answer and explanation
Correct option: B
3356\frac{{33}}{{56}}
Option A is correct because by using the given information to find tan⁡(α+β)\tan(\alpha + \beta) and tan⁡(α−β)\tan(\alpha - \beta), we can then find tan⁡2α\tan 2\alpha using the tangent addition formula.
75 Easy
75 of 91
Analyzing +4 | -1
If sin⁡A+sin⁡  B=a\sin A + \sin \;B = a and cos⁡A+cos⁡B=b\cos A + \cos B = b, then cos⁡(A+B)\cos \left( {A + B} \right)
View answer and explanation
Correct option: A
a2+b2b2−a2\frac{{{a^2} + {b^2}}}{{{b^2} - {a^2}}}
Option C (b2−a2a2+b2\frac{{{b^2} - {a^2}}}{{{a^2} + {b^2}}}) is correct because by squaring and manipulating the given equations, we can express cos⁡(A+B)\cos(A+B) in terms of aa and bb.

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
76 Easy
76 of 91
Analyzing +4 | -1
If tan⁡θ+tan⁡(π3+θ)+tan⁡(−π3+θ)=atan⁡3θ,\tan \mathrm{\theta } + \tan \left( {\frac{\pi }{3} + \mathrm{\theta }} \right) + \tan \left( { - \frac{\pi }{3} + \mathrm{\theta }} \right) = a\tan 3\mathrm{\theta }, then aa is equal to
View answer and explanation
Correct option: C
3
Option C (3) is correct because simplifying the trigonometric expression leads to 3tan⁡3θ=atan⁡3θ3\tan 3\theta = a\tan 3\theta, thus a=3a = 3.
77 Easy
77 of 91
Analyzing +4 | -1
If m  tan⁡  (θ−30∘)=n  tan⁡  (θ+120∘)m\,\,\tan \,\,\left( {\theta - 30^\circ } \right) = n\,\,\tan \,\,\left( {\theta + 120^\circ } \right), then cos⁡  2θ\cos \,\,2\theta equals
View answer and explanation
Correct option: D
m+n2(m−n)\frac{{m + n}}{{2\left( {m - n} \right)}}
Option D (m+n2(m−n)\frac{{m + n}}{{2\left( {m - n} \right)}}) is correct because it is the result of simplifying the trigonometric equation and solving for cos⁡2θ\cos 2\theta.
78 Easy
78 of 91
Application +4 | -1
If tan⁡  A\tan \,\,A and tan⁡  B\tan \,\,B are the roots of abx2−c2x+ab=0ab{x^2} - {c^2}x + ab = 0 where a,   b,   ca,\,\;b,\,\;c are the sides of the triangles ABCABC, then the value of sin⁡2A+sin⁡2B+sin⁡2C{\sin ^2}A + {\sin ^2}B + {\sin ^2}C is
View answer and explanation
Correct option: D
2
Option D (2) is correct because, given the roots of the quadratic equation, we can deduce that the triangle is right-angled, and then calculate the value of the expression.
79 Easy
79 of 91
Analyzing +4 | -1
In a Δ PQR,   ∠R=π2\Delta \,PQR,\,\;\angle R = \frac{\pi }{2}. If tan⁡  P2\tan \,\,\frac{P}{2} and tan⁡  Q2\tan \,\,\frac{Q}{2} are the roots of the equation ax2+  bx+c=0(a≠0)a{x^2} + \,\,bx + c = 0\left( {a \ne 0} \right), then
View answer and explanation
Correct option: A
a+b=ca + b = c
Option A (a+b=ca + b = c) is correct because it is derived from the relationship between the roots of the quadratic equation and the fact that P+Q=π2P + Q = \frac{\pi}{2} in the given triangle.
80 Easy
80 of 91
Application +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) 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 it is the simplified result after applying trigonometric identities and algebraic manipulation to the given equations.
81 Easy
81 of 91
Analyzing +4 | -1
In △ABC\triangle A B C, line joining the circumcentre and orthocentre is parallel to side ACA C, then the value of tan⁡A⋅tan⁡C\tan A \cdot \tan C is equal to
View answer and explanation
Correct option: B
3
Option B (3) is correct because by equating the distance of the circumcentre and orthocentre from side AC, we can derive the relation tan⁡A⋅tan⁡C=3\tan A \cdot \tan C = 3.
82 Easy
82 of 91
Application +4 | -1
If tan⁡α=1/7\tan \alpha=1 / 7 and sin⁡β=1/10\sin \beta=1 / \sqrt{10} where 0<α,β<π/20<\alpha, \beta<\pi / 2, then 2β2 \beta is equal to
View answer and explanation
Correct option: A
π/4−α\pi / 4-\alpha
Option A (π4−α\frac{\pi}{4} - \alpha) is correct because by finding tan⁡2β\tan 2\beta and then tan⁡(α+2β)\tan (\alpha + 2\beta), we can determine that α+2β=π4\alpha + 2\beta = \frac{\pi}{4}, leading to 2β=π4−α2\beta = \frac{\pi}{4} - \alpha.
83 Easy
83 of 91
Application +4 | -1
If   tan α,  tan⁡ β,  tan⁡ γ  \mathrm{\;tan}\,\alpha ,\,\,\tan \,\beta ,\,\,\tan \,\gamma \; are the roots of the equation x3−px2−r=0{x^3} - p{x^2} - r = 0, then the value of (1+tan⁡2α)  (1+tan⁡2β)  (1+tan⁡2γ)\left( {1 + {{\tan }^2}\alpha } \right)\,\,\left( {1 + {{\tan }^2}\beta } \right)\,\,\left( {1 + {{\tan }^2}\gamma } \right) is equal to
View answer and explanation
Correct option: B
1+(p−r)21 + {\left( {p - r} \right)^2}
Option B is correct because it represents the simplified expression after applying Vieta's formulas and trigonometric identities to the given equation.
84 Easy
84 of 91
Analyzing +4 | -1
If tan⁡  θ  tan⁡(π3+θ)  tan⁡  (−π3+θ)=k  tan⁡  3θ\tan \,\,\theta \,\,\tan \left( {\frac{\pi }{3} + \theta } \right)\,\,\tan \,\,\left( { - \frac{\pi }{3} + \theta } \right) = k\,\,\tan \,\,3\theta, then the value of kk is
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the simplification of the given expression results in k=−1k = -1, which is not among the provided options.
85 Easy
85 of 91
Application +4 | -1
If A+C=BA+C=B, then tan⁡Atan⁡Btan⁡C\tan A \tan B \tan C is equal to
View answer and explanation
Correct option: B
tan⁡B−tan⁡C−tan⁡A\tan B-\tan C-\tan A
Option B (tan B - tan C - tan A) is correct because it is derived from applying the tangent addition formula and rearranging the terms.
86 Easy
86 of 91
Application +4 | -1
sin⁡A+sin⁡  B=3  (cos⁡  B−cos⁡  A)⇒sin⁡  3A+sin⁡  3B\sin A + \sin \,\,B = \sqrt 3 \,\,\left( {\cos \,\,B - \cos \,\,A} \right) \Rightarrow \sin \,\,3A + \sin \,\,3B is equal to
View answer and explanation
Correct option: A
0\mathrm{0}
Option A (0\mathrm{0}) is correct because simplifying the given condition leads to A=−BA = -B, and thus sin⁡3A+sin⁡3B=0\sin 3A + \sin 3B = 0.
87 Easy
87 of 91
Application +4 | -1
If cos⁡(A−B)=35\cos \left( {A - B} \right) = \frac{3}{5} and tan⁡A  tan⁡B=2\tan A\,\,\tan B = 2, then
View answer and explanation
Correct option: A
cos⁡A  cos⁡B=15\cos A\,\,\cos B = \frac{1}{5}
Option A (cos A cos B = 1/5) is correct because, given the conditions, solving for tan A and tan B allows us to find cos A cos B = 1/5.
88 Easy
88 of 91
Application +4 | -1
If cot⁡α=1\cot \alpha=1 and sec⁡β=−53\sec \beta=-\frac{5}{3}, where π<α<3π2\pi<\alpha<\frac{3 \pi}{2} and π2<β<π\frac{\pi}{2}<\beta<\pi, then the value of tan⁡(α+\tan (\alpha+ β)\beta) and the quadrant in which α+β\alpha+\beta lies, respectively are :
View answer and explanation
Correct option: A
−17-\frac{1}{7} and IVth quadrant
The correct answer is A (-1/7 and IVth quadrant) because it correctly calculates the tangent of the sum of angles and identifies the correct quadrant.
89 Easy
89 of 91
Application +4 | -1
The value of tan⁡  70∘−tan⁡  20∘tan⁡  50∘\frac{{\tan \,\,70^\circ - \tan \,\,20^\circ }}{{\tan \,\,50^\circ }} is equal to
View answer and explanation
Correct option: A
2
Option A (2) is correct because simplifying the trigonometric expression using the tangent addition formula and complementary angle identities results in the value 2.
90 Easy
90 of 91
Application +4 | -1
If A+B+C=0A + B + C = 0, then the value of ∑cot⁡(B+C−A)cot⁡(C+A−B)\sum \cot \left( {B + C - A} \right)\cot \left( {C + A - B} \right) is equal to
View answer and explanation
Correct option: B
1
Option B (1) is correct because by using the condition A + B + C = 0, the expression simplifies to a known trigonometric identity which equals 1.
Revision notes and key takeaways

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

Showing 61-90 of 91 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - COMPOUND ANGLES MCQs (All) 147 MCQs → ENGINEERING MATHEMATICS - COMPOUND ANGLES MCQs (Hard) 5 MCQs → ENGINEERING MATHEMATICS - COMPOUND ANGLES MCQs (Medium) 51 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

Your practice

0 / 91 answered · 91 remaining · 0% accuracy

Progress is stored on this device. Sign in to save to your account.

✓ Correct · ✗ Incorrect · ○ Unanswered

Answer feedback and difficulty
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 →