The solution of the equation $\left| {\,\begin{array}{*{20}{c}}{\cos \theta }&{\sin \theta }&{\cos \theta }\\{ - \sin \theta }&{\cos \theta }&{\sin \theta }\\{ - \cos \theta }&{ - \sin \theta }&{\cos \theta }\end{array}\,} \right| = 0$, is
$\theta = n\pi $
$\theta = 2n\pi \pm \frac{\pi }{2}$
$\theta = n\pi \pm {( - 1)^n}\frac{\pi }{4}$
$\theta = 2n\pi \pm \frac{\pi }{4}$
The smallest positive angle which satisfies the equation $2{\sin ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$, is
The general solution of $\sin x - 3\sin 2x + \sin 3x = $ $\cos x - 3\cos 2x + \cos 3x$ is
The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if
The number of solutions of the equation $32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}$ is :
The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is