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

The period of the function $f(x) = \cos 4x + \tan 3x$ is

Let $f(x) = \cos px + \sin x$ be a periodic function,then $p$ must be

The period of $\sin \frac{x}{2} - \cos \frac{x}{3}$ is (in $\pi$)

The period of $f(x) = x - [x]$,if it is periodic,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} = $