If $\sin \theta + \cos \theta = \sqrt 2 \cos \alpha $, then the general value of $\theta $ is
$2n\pi - \frac{\pi }{4} \pm \,\,\alpha $
$2n\pi + \frac{\pi }{4} \pm \alpha $
$n\pi - \frac{\pi }{4} \pm \alpha $
$n\pi + \frac{\pi }{4} \pm \alpha $
If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is
Find the principal and general solutions of the equation $\sec x=2$
The number of solutions to the equation $\cos ^4 x+\frac{1}{\cos ^2 x}=\sin ^4 x+\frac{1}{\sin ^2 x}$ in the interval $[0,2 \pi]$ is
If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
Find the general solution of the equation $\sin 2 x+\cos x=0$