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

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 $\tanh x = \frac{1}{2}$,then $\sinh 2x - \text{sech } 2x = $

If $\cos \theta + \sin \theta = \sqrt{2} \cos \theta$ and $0 < \theta < \frac{\pi}{2}$,then $\sec 2 \theta + \tan 2 \theta = $

If $A$ and $B$ are positive acute angles satisfying $3 \cos^2 A + 2 \cos^2 B = 4$ and $\frac{3 \sin A}{\sin B} = \frac{2 \cos B}{\cos A}$,then $A + 2B =$ (in $^{\circ}$)

If $P = \tan 15^{\circ} + \cot 15^{\circ}$,$Q = \tan 22 \frac{1}{2}^{\circ} + \cot 22 \frac{1}{2}^{\circ}$ and $R = \sin 54^{\circ} + \sin 18^{\circ}$,then their ascending order is