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

The minimum value of $(8 \sec^2 \theta + 2 \cos^2 \theta)$ is equal to :-

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...........

In a triangle,if $\tan A + \tan B + \tan C = 6$ and $\tan A \tan B = 2$,then the values of $\tan A, \tan B,$ and $\tan C$ are:

The minimum value of $f(x) = a^{a^{x}} + a^{1-a^{x}}$,where $a, x \in R$ and $a > 0$,is equal to ..... .

If $5 \cos x + 12 \cos y = 13$,then the maximum value of $5 \sin x + 12 \sin y$ is: