If A is an acute angle, which of the following is equal to

To simplify the trigonometric expression (sin A) / (1 + cos A), we can use half-angle identities.

Step-by-Step Simplification
Use Trigonometric Identities:

sin A = 2 * sin(A/2) * cos(A/2)

cos A = 2 * cos²(A/2) - 1

Substitute these into the expression:
(2 * sin(A/2) * cos(A/2)) / (1 + (2 * cos²(A/2) - 1))

Simplify the denominator:
The 1 and -1 cancel out, leaving:
(2 * sin(A/2) * cos(A/2)) / (2 * cos²(A/2))

Cancel common terms:
The 2s cancel, and one cos(A/2) cancels out from the numerator and denominator:
sin(A/2) / cos(A/2) = tan(A/2)