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

If $\sin A = n\sin B,$ then $\frac{{n - 1}}{{n + 1}}\tan \,\frac{{A + B}}{2} = $

If $\tan \,(A + B) = p,\,\,\tan \,(A - B) = q,$ then the value of $\tan \,2A$ in terms of $p$ and $q$ is

$96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$ is equal to$......$.

If $x + \frac{1}{x} = 2\,\cos \theta ,$ then ${x^3} + \frac{1}{{{x^3}}} = $

The value of $sin\,10^o$ $sin\,30^o$ $sin\,50^o$ $sin\,70^o$ is