If $\cos \,x = \frac{{2\cos y - 1}}{{2 - \cos y}},x,\,y\, \in \,\left( {0,\pi } \right),$ then $tan(x/2)cot(y/2) =$
$\sqrt 2$
$\sqrt 3$
$1/\sqrt 2$
$1/\sqrt 3$
The number of solutions to the equation $\cos ^4 x+\frac{1}{\cos ^2 x}=\sin ^4 x+\frac{1}{\sin ^2 x}$ in the interval $[0,2 \pi]$ is
If $\cos 2\theta + 3\cos \theta = 0$, then the general value of $\theta $ is
If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is
If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$
The sides of a triangle are $\sin \alpha ,\,\cos \alpha $ and $\sqrt {1 + \sin \alpha \cos \alpha } $ for some $0 < \alpha < \frac{\pi }{2}$. Then the greatest angle of the triangle is.....$^o$