The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is
$\theta = n\pi + \frac{\pi }{2} - \alpha $
$\theta = n\pi - \frac{\pi }{2} + \alpha $
$\theta = n\pi + \frac{\pi }{2} + \alpha $
$\theta = n\pi - \frac{\pi }{2} - \alpha $
Let $A = \left\{ {\theta \,:\,\sin \,\left( \theta \right) = \tan \,\left( \theta \right)} \right\}$ and $B = \left\{ {\theta \,:\,\cos \,\left( \theta \right) = 1} \right\}$ be two sets. Then
If $\frac{{1 - \cos 2\theta }}{{1 + \cos 2\theta }} = 3$, then the general value of $\theta $ is
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.....$^o$
If $\sqrt 3 \tan 2\theta + \sqrt 3 \tan 3\theta + \tan 2\theta \tan 3\theta = 1$, then the general value of $\theta $ is
The general solution of the equation $(\sqrt 3 - 1)\sin \theta + (\sqrt 3 + 1)\cos \theta = 2$ is