Let $f(x) = \cos \sqrt {x,} $ then which of the following is true

The number of solution of the equation,$\sum\limits_{r = 1}^5 {\cos (r\,x)} $ $= 0$ lying in $(0, \pi)$ is :

The values of $\theta $ satisfying $\sin 7\theta = \sin 4\theta - \sin \theta $ and $0 < \theta < \frac{\pi }{2}$ are

Let $A = \left\{ {\theta \,:\,\sin \,\left( \theta  \right) = \tan \,\left( \theta  \right)} \right\}$ and $B = \left\{ {\theta \,:\,\cos \,\left( \theta  \right) = 1} \right\}$ be two sets. Then

The real roots of the equation $cos^7x\,  +\,  sin^4x\,  =\,  1$  in the interval $(-\pi, \pi)$ are

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.