If cos^ 2 θ − sin^2 θ = tan^2 ϕ then which of the following is true?

cos²θ - sin²θ = tan²Φ

 \(\frac{cos²θ - sin²θ}{1}\) =  \(\frac{sin²Φ}{cos²Φ}\)

\(\frac{cos²θ - sin²θ}{cos²θ +sin²θ}\) =  \(\frac{sin²Φ}{cos²Φ}\)

Using componendo and dividendo,

\(\frac{cos²θ }{-sin²θ}\) =  \(\frac{sin²Φ + cos²Φ}{sin²Φ - cos²Φ}\)

\(\frac{sin²θ }{cos²θ}\) =  \(\frac{cos²Φ - sin²Φ}{sin²Φ + cos²Φ}\)

tan²θ = cos²Φ - sin²Φ