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Simplify the expression cos(A) / (1 + sin(A)).

1. tan(45 deg + A/2)
2. tan(45 deg - A/2)
3. cot(45 deg + A/2)
4. tan(A/2)

Correct answer: tan(45 deg - A/2)

Solution

Using half-angle forms, cos(A)/(1+sin(A)) = (cos(A/2)-sin(A/2))/(cos(A/2)+sin(A/2)) = (1-tan(A/2))/(1+tan(A/2)) = tan(45 deg - A/2).

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