If $\cos A = \frac{\sqrt{3}}{2},$ then $\tan 3A = $

If $\sin x - \sin y = \frac{1}{2}$ and $\cos x - \cos y = 1$,then $\tan(x + y)$ is equal to

If $\frac{2\sin \alpha}{1 + \cos \alpha + \sin \alpha} = y$,then $\frac{1 - \cos \alpha + \sin \alpha}{1 + \sin \alpha} = $

If $L = \sin^{2}\left(\frac{\pi}{16}\right) - \sin^{2}\left(\frac{\pi}{8}\right)$ and $M = \cos^{2}\left(\frac{\pi}{16}\right) - \sin^{2}\left(\frac{\pi}{8}\right)$,then which of the following is correct?

Evaluate: $\sin(22 \frac{1}{2}^{\circ})$

$\tan A + 2 \tan 2A + 4 \tan 4A + 8 \cot 8A = $