Pre-Calc question re: polar/rectangular equations?

Question

I'm stuck on this question:

I need to convert this rectangular equation,
x² - y²= 1,
into a polar coordinate equation. I know that it can equal
r²cos²φ - r²sin² φ = 1,
which is also equal to
r² (cos²φ - sin²φ) = 1,
but I don't know what to do from here. Can you help me out?

Answer 1

make cos²φ - sin²φ = cos(2φ)

r = sqrt(sec2φ)

Answer 2

Using the trig identity, cos 2t = cos2 t – sin2 t,
r^2(cos(2φ)) = 1
r = 1/√cos(2φ)