TITLE: What is the period of $f(x) = \sin^4(x)+ \cos^4(x)$?
QUESTION [6 upvotes]: This is an elementary problem but I'm just not getting the right answer.
My reasoning is as follows:
The period of $g(x) = \sin^4(x)$ is $\pi$ and that of $h(x) = \cos^4(x)$ is $π$ as well, so the period of the function $f(x) = \sin^4(x) + \cos^4(x)$ should be the LCM, which would be $\pi$. Plotting the function, however, shows that the period is $\frac{\pi}{2}$. 
Why is that? What am I missing here? I'm sorry if this is trivial, but I'm not able to figure it out.

REPLY [3 votes]: $$\sin^4x+\cos^4x=(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x=1-\frac12\sin^22x$$
as a result has a period of:
$$\frac{2\pi}{4}=\frac{\pi}{2}$$