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
If $\operatorname{cosec}^2(\alpha+\beta)-\sin ^2(\beta-\alpha)+\sin ^2(2 \alpha-\beta)=\cos ^2(\alpha-\beta)$ where $\alpha, \beta \in\left(0, \frac{\pi}{2}\right)$, then $\sin (\alpha-\beta)$ is equal to
If $\cos 3x + \sin \left( {2x - \frac{{7\pi }}{6}} \right) = - 2$, then $x = $ (where $k \in Z$)
The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is
The equation $\sin x\cos x = 2$ has
Find the general solution of $\cos ec\, x=-2$