If $a \cos \theta + b \sin \theta = m$ and $a \sin \theta - b \cos \theta = n$, then what is the relationship between $a, b, m,$ and $n$?

Options:

• A: $a^2 + b^2 = m^2 - n^2$
• B: $a^2 - b^2 = m^2 + n^2$
• C: $a^2 + b^2 = m^2 + n^2$
• D: $a^2 - b^2 = m^2 - n^2$

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