The period of $\cos (3x + 5) + 7$ is

The period of $\frac{\sin \theta + \sin 2\theta}{\cos \theta + \cos 2\theta}$ is

Which of the following function$(s)$ is/are periodic?

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:

The period of $|2\sin 3\theta + 4\cos 3\theta |$ 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