If the solution of the equation $\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right), \quad$ is $\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$, where $\alpha, \beta$ are integers, then $\alpha+\beta$ is equal to:

The solution set of the equation $tan(\pi\, tanx) = cot(\pi\, cot\, x)$ is

The value of the expression

$\frac{{\left (sin 36^o + cos 36^o - \sqrt 2  sin 27^o)( {\sin {{36}^0} + \cos {{36}^0} - \sqrt 2 \sin {{27}^0}} \right)}}{{2\sin {{54}^0}}}$ is less than

For $n \in Z$ , the general solution of the equation

$(\sqrt 3  - 1)\,\sin \,\theta \, + \,(\sqrt 3  + 1)\,\cos \theta \, = \,2$ is

Find the general solution of the equation $\sin x+\sin 3 x+\sin 5 x=0$

Let $f(x) = \cos \sqrt {x,} $ then which of the following is true