Simplify each expression.
sin 158.2°/(1 + cos 158.2°)

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Recognize that the expression \( \frac{\sin 158.2^\circ}{1 + \cos 158.2^\circ} \) can be simplified using trigonometric identities related to half-angle formulas or sum-to-product formulas.

Recall the identity for tangent of half an angle: \( \tan \frac{\theta}{2} = \frac{\sin \theta}{1 + \cos \theta} \). This matches the form of the given expression.

Apply the identity by setting \( \theta = 158.2^\circ \), so the expression simplifies to \( \tan \frac{158.2^\circ}{2} \).

Calculate the half-angle: \( \frac{158.2^\circ}{2} = 79.1^\circ \), so the expression becomes \( \tan 79.1^\circ \).

Thus, the simplified form of the original expression is \( \tan 79.1^\circ \).

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