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If acosθ + bsinθ = m and asinθ - bcosθ = n, prove that a2 + b2 = m2 + n2

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 m2 + n= (acosθ + bsinθ)2 + (asinθ - bcosθ)2

= a2cos2θ + b2sin2θ + 2abcosθsinθ + a2sin2θ + b2cos2θ - 2abcosθsinθ

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

= a2 x 1 + b2 x 1

a+  b2

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