If asintheta+ bcostheta =n
N ,acostheta+ bsintheta = m
Prove :- m?+n?= a?+b?

Dear student,

Given:-m=acosθ-bsinθS.B.Sm2=acosθ-bsinθ2m2=a2cos2θ+b2sin2θ-2absinθcosθ                --(1)       --[using a-b2=a2+b2-2ab]Also givenn=asinθ+bcosθS.B.Sn2=asinθ+bcosθ2n2=a2sin2θ+b2cos2θ+2absinθcosθ                 --(2)      --[using a+b2=a2+b2+2ab]m2+n2=a2cos2θ+sin2θ+b2sin2θ+cos2θ-2absinθcosθ +2absinθcosθ m2+n2=a2+b2                           --[using cos2θ+sin2θ=1]Hence proved
Regards

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