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

If $\sin \theta  = \frac{1}{2}\left( {\sqrt {\frac{x}{y}\,}  + \,\sqrt {\frac{y}{x}} } \right)\,,\,\left( {x,y \in R\, - \{ 0\} } \right)$. Then

$2{\cos ^2}\theta - 2{\sin ^2}\theta = 1$, then $\theta  =$ .......$^o$

If $\alpha $ and $\beta $ are solutions of $sin^2\,x + a\, sin\, x + b = 0$ as well that of $cos^2\,x + c\, cos\, x + d = 0$ , then $sin\,(\alpha + \beta )$ is equal to

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

$1 + \cos \,{56^o} + \cos \,{58^o} - \cos {66^o} = $