TITLE: Solve $\cos^2x-\sin^2x= 1$
QUESTION [20 upvotes]: 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?

REPLY [2 votes]: Maximum value of $\cos^2(x)$ = $1$
Minimum value of $\sin^2(x)$ = $0$
So this is the only case where you get $\cos^2(x) - \sin^2(x) = 1$.
Hence $\cos^2(x) = 1$ and $\sin^2(x) = 0$ => $x = nπ$
Or you could have used the formula : $\cos^2(x) - \sin^2(x) = \cos(2x)$
Hope the answer is clear !