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Simplify the expression (1 + sin theta - cos theta)/(1 + sin theta + cos theta).

1. tan theta/2
2. cot theta/2
3. tan theta
4. sin theta/2

Correct answer: tan theta/2

Solution

Half-angle forms factor numerator and denominator with a common factor (sin(theta/2) + cos(theta/2)); cancelling gives tan(theta/2).

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