The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21$ $-4 \cos ^{2} x$ holds, is
$2$
$7$
$5$
$4$
The general solution of the equation $(\sqrt 3 - 1)\sin \theta + (\sqrt 3 + 1)\cos \theta = 2$ is
Find the general solution of $\cos ec\, x=-2$
The roots of the equation $1 - \cos \theta = \sin \theta .\sin \frac{\theta }{2}$ is
If $2{\cos ^2}x + 3\sin x - 3 = 0,\,\,0 \le x \le {180^o}$, then $x =$
If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is