Question

How do I express x^2 - y^2 in cylindrical coordinates?

Answer 1

You have:
\[r^2\cos^2(\theta)-r^2\sin^2(\theta)=r^2(\cos^2(\theta)-\sin^2(\theta))=r^2\cos(2\theta)\]
Using the identity:
\[\cos(2x)=\cos^2(x)-\sin^2(x)\]