Answer
$$\frac{\sin158.2^\circ}{1+\cos158.2^\circ}=\tan79.1^\circ$$
Work Step by Step
$$\frac{\sin158.2^\circ}{1+\cos158.2^\circ}$$
From the half-angle identity for tangents:
$$\frac{\sin A}{1+\cos A}=\tan\frac{A}{2}$$
We can apply the identity to the given expression with $A=158.2^\circ$.
$$\frac{\sin158.2^\circ}{1+\cos158.2^\circ}=\tan\frac{158.2^\circ}{2}$$
$$\frac{\sin158.2^\circ}{1+\cos158.2^\circ}=\tan79.1^\circ$$
