The period of the function $f(x) = e^{\log(\sin x)} + (\tan x)^3 - \operatorname{cosec}(3x - 5)$ is

The period of $f(x) = nx + n - [nx + n]$,where $n \in N$ and $[ \cdot ]$ denotes the greatest integer function,is:

The period of the function $f(x) = \log(\cos 2x) + \sin 4x$ is :-

If the period of the function $f(x) = \sin 5x \cos 3x$ is $\alpha$,then $\cos \alpha =$

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

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} = $