Question

Prove that: `(1 - tan^2 θ)/(1 + tan^2 θ) = cos^2 θ - sin^2 θ`

Answer 1

LHS = `(1 - tan^2 θ)/(1 + tan^2 θ)`

= `(1 - tan^2 θ)/(sec^2 θ)`

= `1/(sec^2 θ) - (tan^2 θ)/(sec^2 θ)`

= `cos^2 θ - (sin^2 θ)/(cos^2 θ) xx cos^2 θ `

= cos² θ – sin² θ

= RHS

Hence Proved.