Answer
$$\cos2x=\cos^2 x-\sin^2 x$$
The formula is proved to be an identity.
Work Step by Step
$$\cos2x=\cos^2 x-\sin^2 x$$ $$\cos(x+x)=\cos^2 x-\sin^2 x$$
According to the identity of cosine of a sum, we can analyze the left side as follows: $$\cos(x+x)$$ $$=\cos x\cos x-\sin x\sin x$$ $$=\cos^2x-\sin^2x$$
Which means the left side is equal with the right side. So the formula is verified to be an identity.
