$$1+\cos 2x-\cos^2x=\cos^2x$$ This equation is an identity, which can be proved by transforming the left side using the identity from Exercise 69.
Work Step by Step
$$1+\cos 2x-\cos^2x=\cos^2x$$ We examine from the left side: $$A=1+\cos 2x-\cos^2x$$ The question hints at using the result from Question 69, which states that $$\cos 2x=\cos^2x-\sin^2x$$ That means we can replace $\cos2x$ in $A$ with $\cos^2x-\sin^2x$. $$A=1+\cos^2x-\sin^2x-\cos^2x$$ $$A=1-\sin^2 x$$ Now recall that $\cos^2\theta=1-\sin^2\theta$. So, $$A=\cos^2x$$ The equation has been verified to be an identity.