# Trigonometric functions

I wonder how does a WolframAlpha get this relation where input is a LHS and output is RHS:

$$\cos^2(x)\cos(2x) = \tfrac{1}{4}\cos(4x) + \tfrac{1}{2}\cos(2x) + \tfrac{1}{4}$$

-
Are you asking how to prove that equality? – Git Gud Aug 2 '13 at 16:50
Express $\cos^2(x)$ in terms of $\cos(2x), \sin(2x)$ and then use product-to-sum. – Scaramouche Aug 2 '13 at 16:52
Yes. I need to know how to get RHS out of LHS. I tried to use the double angle trigonometric identity and it only got more complicated... – 71GA Aug 2 '13 at 16:53
How Alpha gets it is an interesting question. I don't know, but it is likely not the way a human should approach it. – André Nicolas Aug 2 '13 at 17:02

$$cos^2x=\frac{1+cos(2x)}{2}$$ $$cos^2(2x)=?$$