If $r\,\sin \theta = 3,r = 4(1 + \sin \theta ),\,\,0 \le \theta \le 2\pi ,$ then $\theta = $
$\frac{\pi }{6},\frac{\pi }{3}$
$\frac{\pi }{6},\frac{{5\pi }}{6}$
$\frac{\pi }{3},\frac{\pi }{4}$
$\frac{\pi }{2},\pi $
The number of solutions of the equation $\sqrt[3]{{\sin \theta - 1}} + \sqrt[3]{{\sin \theta }} + \sqrt[3]{{\sin \theta + 1}} = 0$ in $[0,4\pi]$ is
The number of values of $\theta $ in $[0, 2\pi]$ satisfying the equation $2{\sin ^2}\theta = 4 + 3$$\cos \theta $ are
The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21$ $-4 \cos ^{2} x$ holds, is
$\alpha=\sin 36^{\circ}$ is a root of which of the following equation
The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is