Question

If tan θ = `p/q,` show that `(p sin θ – q cos θ)/(p sin θ + q cos θ) = (p^2 − q^2)/(p^2 + q^2)`

Answer 1

Given tan⁡ θ = `p/q`

Then sin θ = `p/sqrt(p^2 + q^2) and cos θ = q/sqrt(p^2 + q^2)`    ...[Substitute into the fraction and the same cancellation gives]

`(p^2 − q^2)/(p^2 + q^2)`