$\cos \alpha .\sin (\beta - \gamma ) + \cos \beta .\sin (\gamma - \alpha ) + \cos \gamma .\sin (\alpha - \beta ) = $
$0$
$1/2$
$1$
$4\cos \alpha \cos \beta \cos \gamma $
If ${\cos ^6}\alpha + {\sin ^6}\alpha + K\,{\sin ^2}2\alpha = 1,$ then $K =$
If $\theta $ is an acute angle and $\sin \frac{\theta }{2} = \sqrt {\frac{{x - 1}}{{2x}}} $, then $\tan \theta $ is equal to
The value of ,$\sqrt 3 \, cosec\, 20^o - sec\, 20^o $ is :
If $\alpha + \beta + \gamma = 2\pi ,$ then
$\tan 3A - \tan 2A - \tan A = $