If $\cos A = \frac{3}{4}$, then $32\sin \frac{A}{2}\cos \frac{5}{2}A = $

If $x\cos \theta = y\cos \,\left( {\theta + \frac{{2\pi }}{3}} \right) = z\cos \,\left( {\theta + \frac{{4\pi }}{3}} \right),$ then the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ is equal to

If $\cos A = \cos B\,\,\cos C$and $A + B + C = \pi ,$ then the value of $\cot \,B\,\cot \,C$ is

$\cos \frac{{2\pi }}{{15}}\cos \frac{{4\pi }}{{15}}\cos \frac{{8\pi }}{{15}}\cos \frac{{16\pi }}{{15}}  =$

The value of $tan^{-1} (\frac{sin2 -1}{cos2})$ is equal to:-

If $\sin x + \cos x = \frac{1}{5},$ then $\tan 2x$ is