The period of $\sin \theta \cos \theta$ is

The period of the function $f(x) = e^{x - [x] + |\cos \pi x| + |\cos 2\pi x| + \dots + |\cos n\pi x|}$ (where $[.]$ denotes the greatest integer function) is:

Which of the following functions has a period of $2$?

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

The period of $\sin^4 x + \cos^4 x$ is

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