If $\cot (\alpha + \beta ) = 0,$ then $\sin (\alpha + 2\beta ) = $
$\sin \alpha $
$\cos \alpha $
$\sin \beta $
$\cos 2\beta $
If $\sin (A + B) =1 $ and $\cos (A - B) = \frac{{\sqrt 3 }}{2},$ then the smallest positive values of $A$ and $ B$ are
The smallest positive root of the equation $tanx\, -\, x = 0$ lies on
If $\cos \,\alpha + \cos \,\beta = \frac{3}{2}$ and $\sin \,\alpha + \sin \,\beta = \frac{1}{2}$ and $\theta $ is the the arithmetic mean of $\alpha $ and $\beta $ , then $\sin \,2\theta + \cos \,2\theta $ is equal to
Solve $\tan 2 x=-\cot \left(x+\frac{\pi}{3}\right)$
Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-