Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$.

Then $\sum_{\theta \in S } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to

The number of integral value $(s)$ of $'p'$ for which the equation $99\cos 2\theta  - 20\sin 2\theta  = 20p + 35$ , will have a solution is 

The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is

If $2\sin \theta + \tan \theta = 0$, then the general values of $\theta $ are

Find the general solution of the equation $\cos 3 x+\cos x-\cos 2 x=0$

Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$  If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal