Minimum value of the function $f(x) = \left| {\sin \,x + \cos \,x + \tan \,x + \cot \,x + \sec \,x + \ cosec\ x} \right|$ is equal to
$2\sqrt 2$
$2\sqrt 2 - 1$
$2 + 3\sqrt 2 $
$2\sqrt 2 + 1$
If $K = sin^6x + cos^6x$, then $K$ belongs to the interval
The number of solutions of equation $3cos^2x - 8sinx = 0$ in $[0, 3\pi]$ is
The number of solutions of the pair of equations $ 2 \sin ^2 \theta-\cos 2 \theta=0 $, $ 2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is
The number of solutions to $\sin \left(\pi \sin ^2 \theta\right)+\sin \left(\pi \cos ^2 \theta\right)=2 \cos \left(\frac{\pi}{2} \cos \theta\right)$ satisfying $0 \leq \theta \leq 2 \pi$ is
The most general value of $\theta $ satisfying the equations $\tan \theta = - 1$ and $\cos \theta = \frac{1}{{\sqrt 2 }}$ is