JEE MATH APEX

Trigonometry-JEE-Main-PYQ’s

Mathematics Questions

If \frac{\tan(A-B)}{\tan A} + \frac{\sin^2 C}{\sin^2 A} = 1, A, B, C \in (0, \frac{\pi}{2}), then
(A) \tan A, \tan C, \tan B are in A.P.
(B) \tan A, \tan C, \tan B are in G.P.
(C) \tan A, \tan B, \tan C are in G.P.
(D) \tan A, \tan B, \tan C are in A.P.
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The value of \frac{\sqrt{3} \csc 20^\circ - \sec 20^\circ}{\cos 20^\circ \cos 40^\circ \cos 60^\circ \cos 80^\circ} is equal to
(A) 32
(B) 64
(C) 12
(D) 16
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If \cot x = \frac{5}{12} for some x \in (\pi, \frac{3\pi}{2}), then \sin 7x \left(\cos \frac{13x}{2} + \sin \frac{13x}{2}\right) + \cos 7x \left(\cos \frac{13x}{2} - \sin \frac{13x}{2}\right) is equal to
(A) \frac{5}{\sqrt{13}}
(B) \frac{6}{\sqrt{26}}
(C) \frac{4}{\sqrt{26}}
(D) \frac{1}{\sqrt{13}}
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Let \frac{\pi}{2} < \theta < \pi and \cot \theta = -\frac{1}{2\sqrt{2}}. Then the value of \sin \left(\frac{15\theta}{2}\right) (\cos 8\theta + \sin 8\theta) + \cos \left(\frac{15\theta}{2}\right) (\cos 8\theta - \sin 8\theta) is equal to :
(A) \frac{\sqrt{2}-1}{\sqrt{3}}
(B) \frac{\sqrt{2}}{\sqrt{3}}
(C) \frac{1-\sqrt{2}}{\sqrt{3}}
(D) -\frac{\sqrt{2}}{\sqrt{3}}
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The value of \csc 10^{\circ} - \sqrt{3} \sec 10^{\circ} is equal to :
(A) 2
(B) 6
(C) 8
(D) 4
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If for \theta \in \left[ -\frac{\pi}{3}, 0 \right] , the points (x, y) = \left( 3\tan\left(\theta + \frac{\pi}{3}\right), 2\tan\left(\theta + \frac{\pi}{6}\right) \right) lie on xy + \alpha x + \beta y + \gamma = 0 ,
then \alpha^2 + \beta^2 + \gamma^2 is equal to:
(A) 75
(B) 96
(C) 80
(D) 72
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If 10 \sin^4 \theta + 15 \cos^4 \theta = 6 , then the value of \frac{27 \csc^6 \theta + 8 \sec^6 \theta}{16 \sec^8 \theta} is
(A) \frac{2}{5}
(B) \frac{3}{5}
(C) \frac{1}{5}
(D) \frac{3}{4}
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If \sin x + \sin^2 x = 1 , x \in \left(0, \frac{\pi}{2}\right) , then \cos^{12} x + \tan^{12} x + 3( \cos^{10} x + \tan^{10} x + \cos^8 x + \tan^8 x) + (\cos^6 x + \tan^6 x) is equal to:
(A) 3
(B) 4
(C) 2
(D) 1
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If \sum_{r=1}^{13} \left\{ \frac{\sin \left( \frac{\pi}{4} + (r-1) \cdot \frac{\pi}{6} \right)}{\sin \left( \frac{\pi}{4} + r \cdot \frac{\pi}{6} \right)} \right\} = a\sqrt{3} + b , a, b \in \mathbb{Z} ,
then a^2 + b^2 is equal to:
(A) 10
(B) 4
(C) 8
(D) 2
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Let the range of the function f(x) = 6 + 16 \cos x \cdot \cos \left( \frac{\pi}{3} - x \right) \cdot \cos \left( \frac{\pi}{3} + x \right) \cdot \sin 3x \cdot \cos 6x , x \in \mathbb{R} , be $latex[ \alpha, \beta ] $.
Then the distance of the point (\alpha, \beta) from the line 3x + 4y + 12 = 0 is:
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The value of ( \sin 70^\circ) (\cot 10^\circ \cot 70^\circ - 1) is
(A) 0
(B) \(\frac{2}{3}\)
(C) 1
(D) \(\frac{3}{2}\)
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