The most general value of $\theta $ satisfying the equations $\tan \theta = - 1$ and $\cos \theta = \frac{1}{{\sqrt 2 }}$ is
$n\pi + \frac{{7\pi }}{4}$
$n\pi + {( - 1)^n}\frac{{7\pi }}{4}$
$2n\pi + \frac{{7\pi }}{4}$
None of these
General solution of the equation $\cot \theta - \tan \theta = 2$ is
If the equation $2tan\ x \ sin\ x -2 tan\ x + cos\ x = 0$ has $k$ solutions in $[0,k \pi]$, then number of integral values of $k$ 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 number of roots of the equation $\cos ^7 \theta-\sin ^4 \theta=1$ that lie in the interval $[0,2 \pi]$ is
If $\cos p\theta = \cos q\theta ,p \ne q$, then