Q:

Solve $\cos^2x-\sin^2x= 1$

I am trying to solve for $x$ in the following equation:
$$\cos^2x-\sin^2x= 1$$  
Given that $\cos^2x+\sin^2x= 1$, is this something I could use to solve it?

A:

Observe that $\cos^2 x$ never gets bigger than 1.  So if there is a solution, it must have $\cos^2 x = 1$ and $\sin^2 x = 0$. Does that help?

A:

Use the identity $\cos 2x =\cos^2x-\sin^2x$.

A:

You could indeed use that, since then $$\cos^2x-\sin^2x=\cos^2x+\sin^2x.$$ Gather all your trig terms on one side, and the rest is almost trivial.

