JEE MATH APEX

Trigonometry-JEE-Main-PYQ’s

If \sin^2(10^\circ) \sin(20^\circ) \sin(40^\circ) \sin(50^\circ) \sin(70^\circ) = \alpha - \frac{1}{16} \sin(10^\circ), then 16 + \alpha^{-1} is equal to
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The number of integral values of k for which the equation 3 \sin x + 4 \cos x = k + 1 has a solution, k \in \mathbb{R} , is
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If \frac{\sqrt{2} \sin \alpha}{\sqrt{1 + \cos 2\alpha}} = \frac{1}{7} \quad \text{and} \quad \sqrt{\frac{1 - \cos 2\beta}{2}} = \frac{1}{\sqrt{10}}

\alpha, \beta \in \left(0, \frac{\pi}{2}\right)

then \tan(\alpha + 2\beta) \text{ is equal to } \_\_\_\_\_.
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