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
$8$
$9$
$10$
$11$
The general solution of $sin\, x + sin \,5x = sin\, 2x + sin \,4x$ is :
If $\cos \theta + \cos 7\theta + \cos 3\theta + \cos 5\theta = 0$, then $\theta $
If the sum of solutions of the system of equations $2 \sin ^{2} \theta-\cos 2 \theta=0$ and $2 \cos ^{2} \theta+3 \sin \theta=0$ in the interval $[0,2 \pi]$ is $k \pi$, then $k$ is equal to.
If $K = sin^6x + cos^6x$, then $K$ belongs to the interval
If $5{\cos ^2}\theta + 7{\sin ^2}\theta - 6 = 0$, then the general value of $\theta $ is