The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is
$2n\pi + \frac{\pi }{3},\,n \in I$
$n\pi + \frac{\pi }{2},\,n \in I$
$n\pi + \frac{\pi }{4},\,n \in I$
$2n\pi - \frac{\pi }{3},\,n \in I$
The number of solutions of $sin \,3x\, = cos\, 2x$ , in the interval $\left( {\frac{\pi }{2},\pi } \right)$ is
All possible values of $\theta \in[0,2 \pi]$ for which $\sin 2 \theta+\tan 2 \theta>0$ lie in
The number of solutions to $\sin x=\frac{6}{x}$ with $0 \leq x \leq 12 \pi$ is
If $4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 $, then the general value of $\theta $ is
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.