The period of $\cot 3x - \cos (4x + 3)$ is

Let $f$ and $g$ be periodic functions with the periods $T_{1}$ and $T_{2}$ respectively. Then $f+g$ is

Let $f(x) = \sin x + \cos(ax)$ be a periodic function. Then:

Consider the function $f(x) = \cos(x^2)$. Then,

Let $f(x) = \sin^2 x + \cos^4 x + 2$ and $g(x) = \cos(\cos x) + \cos(\sin x)$. Also,let the period of $f(x)$ and $g(x)$ be $T_1$ and $T_2$ respectively,then:

If $f(x) = \sin^2\left(\frac{\pi}{8} + \frac{x}{2}\right) - \sin^2\left(\frac{\pi}{8} - \frac{x}{2}\right)$,then the period of $f$ is