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If $a \cos θ + b \sin θ = m$ and $a \sin θ - b \cos θ = n$ , then $a^{2} + b^{2} =$

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m^{2} - n^{2}

m^{2} n^{2}

n^{2} - m^{2}

m^{2} + n^{2}

answer is D.

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Detailed Solution

a \cos θ + b \sin θ = m

$a^{2} \cos^{2} θ + b^{2} \sin^{2} θ + 2 a b \cos θ \sin θ = m^{2}$

$a \sin θ - b \cos θ = n$

$a^{2} \sin^{2} θ + b^{2} \cos^{2} θ - 2 a b \cos θ \sin θ = n^{2}$

$a^{2} + b^{2} = m^{2} + n^{2}$

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