If $cosA + cosB = cosC,\ sinA + sinB = sinC$ then the value of expression $\frac{{\sin \left( {A + B} \right)}}{{\sin 2C}}$ is

In any triangle $ABC ,$ ${\sin ^2}\frac{A}{2} + {\sin ^2}\frac{B}{2} + {\sin ^2}\frac{C}{2}$ is equal to

Prove that $\frac{\cos 4 x+\cos 3 x+\cos 2 x}{\sin 4 x+\sin 3 x+\sin 2 x}=\cot 3 x$

$cosec^2\theta $ = $\frac{4xy}{(x +y)^2}$ is true if and only if

For any $\theta \, \in \,\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$, the expression $3\,{\left( {\sin \,\theta  - \cos \,\theta } \right)^4} + 6{\left( {\sin \,\theta  + \cos \,\theta } \right)^2} + 4\,{\sin ^6}\,\theta $ equals

If $90^\circ < A < 180^\circ $ and $\sin A = \frac{4}{5},$ then $\tan \frac{A}{2}$ is equal to