If $\cos 2\theta = (\sqrt 2 + 1)\,\,\left( {\cos \theta - \frac{1}{{\sqrt 2 }}} \right)$, then the value of $\theta $ is
$2n\pi + \frac{\pi }{4}$
$2n\pi \pm \frac{\pi }{4}$
$2n\pi - \frac{\pi }{4}$
None of these
Minimum value of the function $f(x) = \left| {\sin \,x + \cos \,x + \tan \,x + \cot \,x + \sec \,x + \ cosec\ x} \right|$ is equal to
If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is
If $A, B, C, D$ are the angles of a cyclic quadrilateral taken in order, then
$cos(180^o + A) + cos(180^o -B) + cos(180^o -C) -sin(90^o -D)=$
Number of solutions of $\sqrt {\tan \theta } = 2\sin \theta ,\theta \in \left[ {0,2\pi } \right]$ is equal to
Let $S=\left[-\pi, \frac{\pi}{2}\right)-\left\{-\frac{\pi}{2},-\frac{\pi}{4},-\frac{3 \pi}{4}, \frac{\pi}{4}\right\}$. Then the number of elements in the set $=\{\theta \in S : \tan \theta(1+\sqrt{5} \tan (2 \theta))=\sqrt{5}-\tan (2 \theta)\}$ is $...$