Question

If pcotθ = q, examine whether psin θ-qcosθ/psin θ+qcosθ=p²-q²/p²+q²

Answer 1

Solve this as shown in the attachment.

Answer 2

pcotθ = q => tanθ = p/q

LHS = (psinθ - qcosθ)/(psinθ + qcosθ)

dividing by cosθ from numerator and denominator.

= (psinθ/cosθ - qcosθ/cosθ)/(psinθ/cosθ + qcosθ/cosθ)

= (ptanθ - q)/(ptanθ + q)

now putting tanθ = p/q

= (p × p/q - q)/(p × p/q + q)

= (p² + q²)/(p² - q²) = RHS