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 . . .
$7$
$9$
$3$
$5$
If ${\sec ^2}\theta = \frac{4}{3}$, then the general value of $\theta $ is
If the equation $\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0$ has real solutions for $\theta,$ then $\lambda$ lies in the interval
If the equation $2tan\ x \ sin\ x -2 tan\ x + cos\ x = 0$ has $k$ solutions in $[0,k \pi]$, then number of integral values of $k$ is-
Find the principal and general solutions of the question $\tan x=\sqrt{3}$.
The general value $\theta $ is obtained from the equation $\cos 2\theta = \sin \alpha ,$ is