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 $
If $sin\, \theta = sin\, \alpha$ then $sin\, \frac{\theta }{3}$ =
If $2(\sin x - \cos 2x) - \sin 2x(1 + 2\sin x)2\cos x = 0$ then
The number of solutions of the equation $32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}$ is :
The number of solutions of the equation $\sin x=$ $\cos ^{2} x$ in the interval $(0,10)$ is
The equation, $sin^2 \theta - \frac{4}{{{{\sin }^3}\,\,\theta \,\, - \,\,1}} = 1$$ -\frac{4}{{{{\sin }^3}\,\,\theta \,\, - \,\,1}}$ has :