The general solution of the trigonometric equation $tan\, x + tan \,2x + tan\, 3x = tan \,x · tan\, 2x · tan \,3x$ is
$x = n\pi$
$n\pi ± \frac{\pi }{3}$
$x = 2n\pi$
$x = \frac{{n\pi }}{3}$ where $n \in I$
The number of elements in the set $S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$ is $...........$.
If $\sin 5x + \sin 3x + \sin x = 0$, then the value of $x$ other than $0$ lying between $0 \le x \le \frac{\pi }{2}$ is
If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is
If $\cos \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1$, then the general value of $\theta $ is
If $\cot \theta + \tan \theta = 2{\rm{cosec}}\theta $, the general value of $\theta $ is