The period of $\sin \theta - \sqrt{3} \cos \theta$ is

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

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 $f(x) = \frac{2 \sin \left(\frac{\pi x}{3}\right) \cos \left(\frac{2 \pi x}{5}\right)}{3 \tan \left(\frac{7 \pi x}{2}\right) - 5 \sec \left(\frac{5 \pi x}{3}\right)}$ is

If $f: R \rightarrow R$ is defined by $f(x) = 7 + \cos(5x + 3)$ for $x \in R$,then the period of $f$ is

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