The maximum value of the function $f(x) = 3\sin x + 4\cos x$ is

The value of $\sum_{r=1}^{18} \cos^2(5r)^\circ$,where $x^\circ$ denotes the $x$ degree,is equal to

If $\sin x + \cos x = a$,$a \in [-\sqrt{2}, \sqrt{2}] - \{-1, 1\}$,then $\sum_{n=1}^\infty (\sin^n x + \cos^n x)$ is equal to -

If $A, B, C$ are angles of a triangle,then $\sin 2A + \sin 2B - \sin 2C$ is equal to

If $\alpha, \beta, \gamma$ are positive numbers such that $\alpha + \beta = \pi$ and $\beta + \gamma = \alpha$,then $\tan \alpha$ is equal to - (where $\gamma \neq n\pi, n \in I$)

If $\sin A, \cos A$ and $\tan A$ are in $G.P.$,then $\cos^3 A + \cos^2 A$ is equal to