JEE Main 2022 (Online) 26th June Morning Shift

Numerical

-1

If $${\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin (10^\circ )$$, then $$16 + {\alpha ^{ - 1}}$$ is equal to __________.

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JEE Main 2021 (Online) 26th February Morning Shift

Numerical

-1

The number of integral values of 'k' for which the equation $$3\sin x + 4\cos x = k + 1$$ has a solution, k$$\in$$R is ___________.

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JEE Main 2020 (Online) 8th January Evening Slot

Numerical

-0

If $${{\sqrt 2 \sin \alpha } \over {\sqrt {1 + \cos 2\alpha } }} = {1 \over 7}$$ and $$\sqrt {{{1 - \cos 2\beta } \over 2}} = {1 \over {\sqrt {10} }}$$

$$\alpha ,\beta \in \left( {0,{\pi \over 2}} \right)$$ then tan($$\alpha $$ + 2$$\beta $$) is equal to _____.

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