No. of solution of equation $sin^{65}x\, -\, cos^{65}x =\, -1$ is, if $x \in (-\pi , \pi )$
$3$
$4$
$2$
$1$
The positive integer value of $n>3$ satisfying the equation $\frac{1}{\sin \left(\frac{\pi}{n}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{n}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{n}\right)}$ is
Find the general solution of $\cos ec\, x=-2$
The general solution of $\frac{{\tan \,2x\, - \,\tan \,x}}{{1\, + \,\tan \,x\,\tan \,2x}}\, = \,1$ is
The number of all possible triplets $(a_1 , a_2 , a_3)$ such that $a_1+ a_2 \,cos \, 2x + a_3 \, sin^2 x = 0$ for all $x$ is
The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is