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
$2 \sqrt{3}$
$\frac{3}{2}$
$\sqrt{3}$
$\frac{1}{2}$
The number of solutions $x$ of the equation $\sin \left(x+x^2\right)-\sin \left(x^2\right)=\sin x$ in the interval $[2,3]$ is
For $x \in(0, \pi)$, the equation $\sin x+2 \sin 2 x-\sin 3 x=3$ has
If $\frac{{1 - {{\tan }^2}\theta }}{{{{\sec }^2}\theta }} = \frac{1}{2}$, then the general value of $\theta $ is
If $(1 + \tan \theta )(1 + \tan \phi ) = 2$, then $\theta + \phi =$ ....$^o$
Find the solution of $\sin x=-\frac{\sqrt{3}}{2}$