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

The minimum value of $27 \tan^2 \theta + 3 \cot^2 \theta$ is

$a, b, c$ are the sides of a scalene triangle $ABC$. If angles $\alpha, \beta, \gamma$ lie between $0$ and $\pi$ such that $\cos \alpha = \frac{a}{b+c}, \cos \beta = \frac{b}{c+a}$ and $\cos \gamma = \frac{c}{a+b}$,then $\tan^2 \frac{\alpha}{2} + \tan^2 \frac{\beta}{2} + \tan^2 \frac{\gamma}{2} =$

In triangle $ABC$,if $\cos A \cos B + \sin A \sin B \sin C = 1$,then $\sin A + \sin B + \sin C =$

If $A, B, C$ are the angles of $\triangle ABC$,then $\cot A \cot B + \cot B \cot C + \cot A \cot C = $

The equation $\sin x(\sin x+\cos x)=k$ has real solutions,where $k$ is a real number. Then,