The number of roots of the equation $\cos ^7 \theta-\sin ^4 \theta=1$ that lie in the interval $[0,2 \pi]$ is
$2$
$3$
$4$
$8$
General solution of the equation $\cot \theta - \tan \theta = 2$ is
If $\sqrt{3}\left(\cos ^{2} x\right)=(\sqrt{3}-1) \cos x+1,$ the number of solutions of the given equation when $x \in\left[0, \frac{\pi}{2}\right]$ is
The number of solution of the equation,$\sum\limits_{r = 1}^5 {\cos (r\,x)} $ $= 0$ lying in $(0, \pi)$ is :
If $|k|\, = 5$ and ${0^o} \le \theta \le {360^o}$, then the number of different solutions of $3\cos \theta + 4\sin \theta = k$ is
The solution of the equation ${\cos ^2}x - 2\cos x = $ $4\sin x - \sin 2x,$ $\,(0 \le x \le \pi )$ is