If $\frac{3\pi}{4} < \alpha < \pi,$ then $\sqrt{\csc^2 \alpha + 2\cot \alpha}$ is equal to

If the sum and difference of two angles are $\pi$ and $\frac{\pi}{12}$ respectively,then the values of the angles in degree measure are (in $^{\circ}$)

The value of $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$ is

If $x \cos \theta = y \cos \left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)$,then the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ is equal to

The value of $\cos 24^{\circ} + \cos 55^{\circ} + \cos 125^{\circ} + \cos 204^{\circ} + \cos 300^{\circ}$ is

The value of $\sin ^{2} 75^{\circ}-\sin ^{2} 15^{\circ}$ is: