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If sin(theta) + sin(phi) = a and cos(theta) + cos(phi) = b, find tan((theta - phi)/2).

1. sqrt((4 - a² - b²)/(a² + b²))
2. sqrt((a² + b²)/(4 - a² - b²))
3. (4 - a² - b²)/(a² + b²)
4. sqrt(4 - a² - b²)

Correct answer: sqrt((4 - a² - b²)/(a² + b²))

Solution

From a² + b² = 2 + 2cos(theta - phi), solving for the half-angle tangent gives sqrt((4 - a² - b²)/(a² + b²)).

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