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Let theta lie in (0deg, 90deg) with sin(theta) = (m² + 2mn)/(m² + 2mn + 2n²). Which expression equals tan(theta)?

1. (m² + 2mn)/(2mn + 2n²)
2. (2mn + 2n²)/(m² + 2mn)
3. (m² + 2mn)/(m² + 2n²)
4. (m² - 2mn)/(2mn + 2n²)

Correct answer: (m² + 2mn)/(2mn + 2n²)

Solution

Computing cos(theta) gives (2mn + 2n²)/D, so tan(theta) = sin/cos = (m² + 2mn)/(2mn + 2n²).

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