Given: x = m sin θ – n cos θ …i) y = m cos θ + n sin θ …ii) Concept: Basic trigonometric identities and algebra Calculation: Squaring equation (i) and (ii) x2 = m2sin2θ+n2cos2θ + 2mn sin θ cos θ …iii) y2 = m2cos2θ+n2sin2θ – 2mn sin θ cos θ …iv) Adding equation (iii) and (iv) ⇒ x2+y2 = m2sin2θ+n2cos2θ + 2mn sin θ cos θ + m2cos2θ+n2sin2θ – 2mn sin θ cos θ ⇒ x2+y2 = m2sin2θ+n2cos2θ + m2cos2θ+n2sin2θ Applying the identity sin2θ+cos2θ = 1 ⇒ x2+y2 = m2+n2