If $A$ lies in the third quadrant and $3\,\tan A - 4 = 0,$ then $5\,\sin 2A + 3\,\sin A + 4\,\cos A = $
$0$
$\frac{{ - 24}}{5}$
$\frac{{24}}{5}$
$\frac{{48}}{5}$
If $a\tan \theta = b$, then $a\cos 2\theta + b\sin 2\theta = $
In any triangle $ABC ,$ ${\sin ^2}\frac{A}{2} + {\sin ^2}\frac{B}{2} + {\sin ^2}\frac{C}{2}$ is equal to
If ${\rm{cosec}}\theta = \frac{{p + q}}{{p - q}},$ then $\cot \,\left( {\frac{\pi }{4} + \frac{\theta }{2}} \right) = $
$\sin {20^o}\,\sin {40^o}\,\sin {60^o}\,\sin {80^o} = $
If $A$ and $B$ are complimentary angles, then :