1
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
If $$\sqrt 3 ({\cos ^2}x) = (\sqrt 3 - 1)\cos x + 1$$, the number of solutions of the given equation when $$x \in \left[ {0,{\pi \over 2}} \right]$$ is __________.
2
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-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 ___________.
3
JEE Main 2020 (Online) 8th January Evening Slot
Numerical
+4
-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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