What is the maximum value of the function $f(x) = \sin x + \cos x$?

In a $\triangle ABC$,suppose none of the angles are multiples of $\frac{\pi}{2}$,then what is the value of $\cot A \cot B + \cot B \cot C + \cot A \cot C$?

If the range of $f(\theta) = \frac{\sin^4 \theta + 3 \cos^2 \theta}{\sin^4 \theta + \cos^2 \theta}$,$\theta \in R$ is $[\alpha, \beta]$,then the sum of the infinite $G.P.$,whose first term is $64$ and the common ratio is $\frac{\alpha}{\beta}$,is equal to...........

If $A+B+C=2S$,then $\sin(S-A)+\sin(S-B)-\sin C=$

The value of $k$,for which $(\cos x + \sin x)^2 + k \sin x \cos x - 1 = 0$ is an identity,is

The minimum value of the function $f(x) = 2\cos 2x - \cos 4x$ in the interval $0 \le x \le \pi$ is: