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If acostheta+bsintheta=m and asintheta-b...

If `acostheta+bsintheta=m` and `asintheta-bcostheta=n ,` Prove that `a^2+b^2=m^2+n^2`

Text Solution

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Given : `acosθ+bsinθ=m ---( 1 )`
asinθ−bcosθ=n ---( 2 )
Squaring (1) and (2), we get
`a^2cos2θ+b^2sin2θ+2absinθcosθ=m^2 ---(3)` ...
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i) If acostheta+bsintheta=m and asintheta-bcostheta=n , then prove that: a^(2)+b^(2)=m^(2)+n^(2)

If acostheta+bsintheta=m and asintheta-bcostheta=n , then show that a^(2)+b^(2)=m^(2)+n^(2) .

Knowledge Check

  • If asintheta+bcostheta=c , find acostheta-bsintheta=?

    A
    `pmsqrt(a^(2)+b^(2)+c^(2))`
    B
    `pmsqrt(a^(2)-b^(2)+c^(2))`
    C
    `pmsqrt(a^(2)+b^(2)-c^(2))`
    D
    none of these

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