How do I find the period if this function?

Question

I need to find the period of $\frac{\cos 3x}{1+\cos2x}$. I know that $\cos3x$ has the period $\frac{2\pi}{3}$ and $\cos2x$ has the period $\pi$, but how do I find the period of that function?

Answer 1

The expression is equivalent to $$2\cos x-\frac 32\sec x$$ and both of these functions have a period of $2\pi$ so the period is $2\pi$