$\operatorname{cosec} 18^{\circ}$ is a root of the equation :

If $\sin x + \sin^{2} x = 1$,then the value of $\cos^{8} x + 2 \cos^{6} x + \cos^{4} x$ is

If $|\sin \alpha - \cos \alpha| = \frac{3}{4}$,then $|\sec 2\alpha - \tan 2\alpha| = $

$\cos^2 76^{\circ} + \cos^2 16^{\circ} - \cos 76^{\circ} \cos 16^{\circ}$ is equal to

Two straight roads intersect at an angle of $60^o$. $A$ bus on one road is $2 \, km$ away from the intersection and a car on the other road is $3 \, km$ away from the intersection. Then the direct distance between the two vehicles is

If $\operatorname{Sinh}^{-1}(2)+\operatorname{Sinh}^{-1}(3)=\alpha$,then $\sinh \alpha=$