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JEE • MATHEMATICS • COMPOUND ANGLES

Compound angles practice · Easy

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31 Easy
31 of 91
Application +4 | -1
If A+C=B{A}+{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\tan B-\tan C-\tan A) is correct because it is derived from applying the tangent addition formula to the equation A + C = B.
32 Easy
32 of 91
Application +4 | -1
tan⁡  2π5−tan⁡  π15−3  tan⁡  2π5tan⁡  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.
33 Easy
33 of 91
Application +4 | -1
tan⁡  25∘+tan⁡  20∘+tan⁡  25∘  tan⁡  20∘\tan \,\,25^\circ + \tan \,\,20^\circ + \tan \,\,25^\circ \,\,\tan \,\,20^\circ is equal to
View answer and explanation
Correct option: A
1
Option A (1) is correct because by using the tangent addition formula and the fact that tan⁡45∘=1\tan 45^\circ = 1, the given expression simplifies to 1.
34 Easy
34 of 91
Application +4 | -1
If A+B+C=180∘A+B+C=180^{\circ}, then the value of tan⁡A+tan⁡B+tan⁡C\tan A+\tan B+\tan C is
View answer and explanation
Correct option: A
≥33\geq 3 \sqrt{3}
Option A (≥33\geq 3 \sqrt{3}) is correct because when A+B+C=180∘A+B+C = 180^{\circ}, tan⁡A+tan⁡B+tan⁡C=tan⁡Atan⁡Btan⁡C\tan A + \tan B + \tan C = \tan A \tan B \tan C, and by AM-GM inequality, the minimum value is 333 \sqrt{3}.
35 Easy
35 of 91
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.
36 Easy
36 of 91
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.
37 Easy
37 of 91
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.
38 Easy
38 of 91
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.
39 Easy
39 of 91
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}.
40 Easy
40 of 91
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.
41 Easy
41 of 91
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.
42 Easy
42 of 91
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.
43 Easy
43 of 91
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.
44 Easy
44 of 91
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.
45 Easy
45 of 91
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.

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46 Easy
46 of 91
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.
47 Easy
47 of 91
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.
48 Easy
48 of 91
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.
49 Easy
49 of 91
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.
50 Easy
50 of 91
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.
51 Easy
51 of 91
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.
52 Easy
52 of 91
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.
53 Easy
53 of 91
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}.
54 Easy
54 of 91
Analyzing +4 | -1
If cos⁡  (θ1−θ2)cos⁡  (θ1+θ2)+cos⁡  (θ3+θ4)cos⁡  (θ3−θ4)=0\frac{{\cos \,\,\left( {{\theta _1} - {\theta _2}} \right)}}{{\cos \,\,\left( {{\theta _1} + {\theta _2}} \right)}} + \frac{{\cos \,\,\left( {{\theta _3} + {\theta _4}} \right)}}{{\cos \,\,\left( {{\theta _3} - {\theta _4}} \right)}} = 0, then tan⁡  θ1  tan⁡  θ2  tan⁡  θ3  tan⁡  θ4=\tan \,\,{\theta _1}\,\,\tan \,\,{\theta _2}\,\,\tan \,\,{\theta _3}\,\,\tan \,\,{\theta _4} =
View answer and explanation
Correct option: C
−1- 1
Option C (-1) is correct because the given condition leads to the relationship tan⁡θ1tan⁡θ2tan⁡θ3tan⁡θ4=−1\tan \theta_1 \tan \theta_2 \tan \theta_3 \tan \theta_4 = -1.
55 Easy
55 of 91
Application +4 | -1
If A+B=π4A + B = \frac{\pi }{4}, then (tan⁡A+1)  (tan⁡B+1)\left( {\tan A + 1} \right)\,\,\left( {\tan B + 1} \right) is equal to
View answer and explanation
Correct option: B
2
Option B (2) is correct because by using the tangent addition formula and the given condition, the expression simplifies to 2.
56 Easy
56 of 91
Application +4 | -1
If A,B,C,D\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D} are the angles of a quadrilaterals then the value of tan⁡A+tan⁡B+tan⁡C+tan⁡Dcot⁡A+cot⁡B+cot⁡C+cot⁡D\frac{\tan A+\tan B+\tan C+\tan D}{\cot A+\cot B+\cot C+\cot D} is
View answer and explanation
Correct option: A
tan⁡Atan⁡Btan⁡Ctan⁡D\tan A \tan B \tan C \tan D
Option A (tan⁡Atan⁡Btan⁡Ctan⁡D\tan A \tan B \tan C \tan D) is correct because it is derived from the trigonometric identities related to the sum of angles in a quadrilateral.
57 Easy
57 of 91
Analyzing +4 | -1
If angle θ\theta be divided into two parts such that the tangent of one part is kk times the tangent of the other and ϕ\phi is their difference, then sinθ\mathrm{sin \theta } is equal to
View answer and explanation
Correct option: A
k+1k−1  sin⁡  ϕ\frac{{k + 1}}{{k - 1}}\,\,\sin \,\,\phi
Option A (k+1k−1 sin⁡ ϕ\frac{{k + 1}}{{k - 1}}\,\sin \,\phi) is correct because by using componendo and dividendo rule on the given condition and applying trigonometric identities, we can express sin⁡θ\sin \theta in terms of kk and sin⁡ϕ\sin \phi.
58 Easy
58 of 91
Application +4 | -1
If α+β=π/2\alpha+\beta=\pi / 2 and β+γ=α\beta+\gamma=\alpha, then tan⁡α\tan \alpha equals
View answer and explanation
Correct option: C
tan⁡β+2tan⁡γ\tan \beta+2 \tan \gamma
Option C (tan⁡β+2tan⁡γ\tan \beta+2 \tan \gamma) is correct because by using the given relations and trigonometric identities, tan⁡α\tan \alpha can be expressed as tan⁡β+2tan⁡γ\tan \beta + 2 \tan \gamma.
59 Easy
59 of 91
Application +4 | -1
If tan⁡θ+tan⁡(π3+θ)+tan⁡(−π3+θ)=Ktan⁡3  θ\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: C
3
Option C (3) is correct because simplifying the given trigonometric expression using tangent addition formulas leads to 3tan⁡3θ3\tan 3\theta, thus K = 3.
60 Easy
60 of 91
Understanding +4 | -1
The value of
cos⁡(45∘−A)cos⁡(45∘−B)−sin⁡(45∘−A)sin⁡(45∘−B)\cos \left(45^{\circ}-A\right) \cos \left(45^{\circ}-B\right)-\sin \left(45^{\circ}-A\right)\sin \left(45^{\circ}-B\right) is
View answer and explanation
Correct option: A
sin⁡(A+B)\sin (A+B)
Option B is correct because using the cosine addition formula, the expression simplifies to cos(90 - (A+B)) which equals sin(A+B).
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