$\sin {163^o}\cos {347^o} + \sin {73^o}\sin {167^o} = $
$0$
$1/2$
$1$
None of these
If $\cos \left( {\alpha + \beta } \right) = \frac{4}{5}$ and $\sin \left( {\alpha - \beta } \right) = \frac{5}{{13}}$,where $0 \le \alpha ,\beta \le \frac{\pi }{4}$ . Then $\tan 2\alpha =$
Prove that $\cot 4 x(\sin 5 x+\sin 3 x)=\cot x(\sin 5 x-\sin 3 x)$
If $\tan \,(A + B) = p,\,\,\tan \,(A - B) = q,$ then the value of $\tan \,2A$ in terms of $p$ and $q$ is
If $A + B + C = \pi \,(A,B,C > 0)$ and the angle $C$ is obtuse then
If $\tan A = \frac{1}{2},\tan B = \frac{1}{3},$ then $\cos 2A = $