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

If $\sin x + \sin^2 x = 1$,then the value of $\cos^{12} x + 3\cos^{10} x + 3\cos^8 x + \cos^6 x - 2$ is equal to

If $\sin A + \sin B = C$ and $\cos A + \cos B = D$,then the value of $\sin (A + B) = $

If $\alpha = 22^\circ 30'$,then $(1 + \cos \alpha )(1 + \cos 3\alpha )(1 + \cos 5\alpha )(1 + \cos 7\alpha )$ equals

$\sin (\beta + \gamma - \alpha ) + \sin (\gamma + \alpha - \beta ) + \sin (\alpha + \beta - \gamma ) - \sin (\alpha + \beta + \gamma ) = $

If $a \cos 2\theta + b \sin 2\theta = c$ has $\alpha$ and $\beta$ as its solutions,then the value of $\tan \alpha + \tan \beta$ is