The general solution of $sin\, x + sin \,5x = sin\, 2x + sin \,4x$ is :
$2n\pi$
$n\pi$
$n\pi /3$
$2 n\pi /3$ where $n \in I$
If $0\, \le \,x\, < \frac{\pi }{2},$ then the number of values of $x$ for which $sin\,x -sin\,2x + sin\,3x=0,$ is
Solve $\tan 2 x=-\cot \left(x+\frac{\pi}{3}\right)$
Let $S$ be the sum of all solutions (in radians) of the equation $\sin ^{4} \theta+\cos ^{4} \theta-\sin \theta \cos \theta=0$ in $[0,4 \pi]$ Then $\frac{8 \mathrm{~S}}{\pi}$ is equal to ...... .
If $\cos \theta + \cos 2\theta + \cos 3\theta = 0$, then the general value of $\theta $ is
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