Why is $2-2\cos(x) = 4\sin^2(\frac{x}{2})$?

Question

As the title states, I was wondering why

$2-2\cos(x) = 4\sin^2(\frac{x}{2})$

holds true?

Answer 1

Use the formulas $\cos (A+B)=\cos A\cos B-\sin A \sin B$ and $\cos^{2}C+\sin ^{2}C=1$. [ Take $A=B=\frac t 2$].