Question

The period of $f\left(x\right)=sin\frac{\pi }{4}\left[x\right]+cos\frac{\pi x}{2}$, where [.] denotes greatest integer function, is___.

Answer 1

Period of $sin\frac{\pi }{4}\left[x\right]$ and $cos\frac{\pi x}{2}$ are 8, 4 respectively so period of $f\left(x\right)=L.C.M.$ (8, 4) = 8