If ${\left( {\frac{{\sin \theta }}{{\sin \phi }}} \right)^2} = \frac{{\tan \theta }}{{\tan \phi }} = 3,$ then the value of $\theta $ and $\phi $ are
$\theta = n\pi \pm \frac{\pi }{3},\,\phi = n\pi \pm \frac{\pi }{6}$
$\theta = n\pi - \frac{\pi }{3},\,\phi = n\pi - \frac{\pi }{6}$
$\theta = n\pi \pm \frac{\pi }{2},\,\phi = n\pi + \frac{\pi }{3}$
None of these
The number of solution of the equation $2\cos ({e^x}) = {5^x} + {5^{ - x}}$, are
The number of solutions of the equation $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2 \pi]$ is
For $n \in Z$ , the general solution of the equation
$(\sqrt 3 - 1)\,\sin \,\theta \, + \,(\sqrt 3 + 1)\,\cos \theta \, = \,2$ is
If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then