The minimum value of $3\sin \theta + 4\cos \theta$ is

The value of $\frac{\sin ^{3} A+\cos ^{3} A}{\sin A+\cos A}+\frac{\cos ^{3} A-\sin ^{3} A}{\cos A-\sin A}$ is

If $x + \frac{1}{x} = 2\cos \theta ,$ then ${x^3} + \frac{1}{{{x^3}}} = $

In the graph of the function $\sqrt{3} \sin x + \cos x$,the maximum distance of a point from the $x$-axis is:

The angle of elevation of the top of a tower is $30^{\circ}$. On walking $100 \ m$ towards the tower,the angle of elevation of the top of the tower becomes $60^{\circ}$. Find the height of the tower (in $m$).

Minimum value of $5 \sin^2 \theta + 4 \cos^2 \theta$ is