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
The solution set of the equation $tan(\pi\, tanx) = cot(\pi\, cot\, x)$ is
The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is
The general solution of ${\sin ^2}\theta \sec \theta + \sqrt 3 \tan \theta = 0$ is
If $\cos 2\theta + 3\cos \theta = 0$, then the general value of $\theta $ is
The sum of solutions of the equation $\frac{\cos \mathrm{x}}{1+\sin \mathrm{x}}=|\tan 2 \mathrm{x}|, \mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)-\left\{\frac{\pi}{4},-\frac{\pi}{4}\right\}$ is :