Answer
$$1+\cos 2x-\cos^2x=\cos^2x$$
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.
