If $4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 $, then the general value of $\theta $ is
$2n\pi \pm \frac{\pi }{3}$
$2n\pi + \frac{\pi }{4}$
$n\pi \pm \frac{\pi }{3}$
$n\pi - \frac{\pi }{3}$
The number of elements in the set $S=$ $\left\{\theta \in[-4 \pi, 4 \pi]: 3 \cos ^{2} 2 \theta+6 \cos 2 \theta-\right.$ $\left.10 \cos ^{2} \theta+5=0\right\}$ is
If $\sin \theta = \sqrt 3 \cos \theta , - \pi < \theta < 0$, then $\theta = $
If $0 \le x < 2\pi $ , then the number of real values of $x,$ which satisfy the equation $\cos x + \cos 2x + \cos 3x + \cos 4x = 0$ is . . .
The solution of the equation $\sec \theta - {\rm{cosec}}\theta = \frac{4}{3}$ is
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then