The general solution of $\cos(x) - \sin(x) = 0$ is

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

If $3 \cos x \neq 2 \sin x$,then the general solution of $\sin ^{2} x-\cos 2 x=2-\sin 2 x$ is

If $0 \le x < \frac{\pi}{2}$,then the number of values of $x$ for which $\sin x - \sin 2x + \sin 3x = 0$ is

Number of solutions of the equation $\cos \theta + \cos 2\theta - \sqrt{3}(\sin \theta + \sin 2\theta) + 1 = 0$ lying in the interval $(0, 2\pi)$ is

If $\cos \theta = -\frac{1}{\sqrt{2}}$ and $\tan \theta = 1$,then the general value of $\theta$ is