Answer :

Given,


a cos θ + b sin θ = m …(1)


a sin θ – b cos θ = n …(2)


Squaring and adding equation 1 and 2, we get –


(a cos θ + b sin θ)2 + (a sin θ – b cos θ)2 = m2 + n2


a2cos2θ + b2sin2θ + 2ab sin θ cos θ + a2sin2θ + b2cos2θ - 2ab sin θ cos θ = m2 + n2


a2cos2θ + b2sin2θ + a2sin2θ + b2cos2θ = m2 + n2


a2(sin2θ + cos2θ) + b2(sin2θ + cos2θ) = m2 + n2


Using: sin2θ + cos2θ = 1, we get –


a2 + b2 = m2 + n2


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