Number of solution $(s)$ of equation $cosec\, \theta -cot \,\theta = 1$ in $[0,2 \pi]$ is-
$4$
$3$
$2$
$1$
If $cosx + secx =\, -2$, then for a $+ve$ integer $n$, $cos^n x + sec^n x$ is
Number of roots of the equation ${\cos ^2}x + \frac{{\sqrt 3 + 1}}{2}\sin x - \frac{{\sqrt 3 }}{4} - 1 = 0$ which lie in the interval $[-\pi,\pi ]$ is
If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is
If ${\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,$ then the general value of $\theta $ is
Let,$S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^{2} \theta}+8^{2 \cos ^{2} \theta}=16\right\}$. Then $n ( S )+\sum_{\theta \in S}\left(\sec \left(\frac{\pi}{4}+2 \theta\right) \operatorname{cosec}\left(\frac{\pi}{4}+2 \theta\right)\right)$ is equal to.