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

The period of the function $f(x) = \cos^2(\sin x) + \sin^2(\cos x)$ is

If $f(x)$ is a periodic function with period $T$,then the function $f(ax + b)$ where $a > 0$,is periodic with period:

If $n \in N$ and the period of $\frac{\cos(nx)}{\sin(x/n)}$ is $4\pi$,then $n$ is equal to

The period of $\cos(x + 8x + 27x + \ldots + n^3x)$ is

Let $\alpha$ be the period of $3 \sin \frac{\pi x}{3} - \cos \frac{\pi x}{2} + \tan \frac{\pi x}{4}$,$\beta$ be the period of $\sin^2 \left( \frac{\pi}{7} + \frac{x}{4} \right) - \sin^2 \left( \frac{\pi}{7} - \frac{x}{4} \right)$,and $\gamma$ be the period of $\cos^4 x + \sin^4 x$. Then $\frac{\alpha \gamma}{\beta} = $