If $0 \le x < 2\pi $ , then the number of real values of $x,$ which satisfy the equation $\cos x + \cos 2x + \cos 3x + \cos 4x = 0$ is . . .
$7$
$9$
$3$
$5$
The number of solutions of the equation $2 \theta-\cos ^{2} \theta+\sqrt{2}=0$ is $R$ is equal to
Number of solutions of equation $sgn(sin x) = sin^2x + 2sinx + sgn(sin^2x)$ in $\left[ { - \frac{{5\pi }}{2},\frac{{7\pi }}{2}} \right]$ is
(where $sgn(.)$ denotes signum function) -
If $\cot \theta + \tan \theta = 2{\rm{cosec}}\theta $, the general value of $\theta $ is
Find the value of $\tan \frac{\pi}{8}$
If $\cos 7\theta = \cos \theta - \sin 4\theta $, then the general value of $\theta $ is