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If acosA + bsinA =m and asinA -bcosA =n ...

If `acosA + bsinA =m` and `asinA -bcosA =n` prove that `a^2+b^2=m^2+n^2`

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`m^2 + n^2 = (acos A + bsin A)^2 + (asinA - bcos A)^2`
`= a^2cos^2 A + b^2sin^2 A + 2ab sinA cos A + a^2sin^2 A + b^2cos^2 A - 2ab sin A cos A`
`= a^2(cos^2A+ sin^2 A) + b^2(cos^2 A + sin^2A)`
`=a^2 +b^2`
hence proved
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