# If a cos θ + b si

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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