If $a{\sin ^2}x + b{\cos ^2}x = c,\,\,$$b\,{\sin ^2}y + a\,{\cos ^2}y = d$ and $a\,\tan x = b\,\tan y,$ then $\frac{{{a^2}}}{{{b^2}}}$ is equal to

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

$\frac{1}{{\tan 3A - \tan A}} - \frac{1}{{\cot 3A - \cot A}} = $

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

$\sqrt 2 + \sqrt 3 + \sqrt 4 + \sqrt 6 $ is equal to

The exact value of $\cos \frac{{2\pi }}{{28}}\,\cos ec\frac{{3\pi }}{{28}}\, + \,\cos \frac{{6\pi }}{{28}}\,\cos ec\frac{{9\pi }}{{28}} + \cos \frac{{18\pi }}{{28}}\cos ec\frac{{27\pi }}{{28}}$ is equal to