Answer
$$\cot\frac{A}{2}=\frac{1+\cos A}{\sin A}$$
Work Step by Step
$$\tan\frac{A}{2}=\frac{\sin A}{1+\cos A}$$
- From Reciprocal Identities, we have:
$$\cot\theta=\frac{1}{\tan\theta}$$
Therefore, we can apply the identity for angle $\frac{A}{2}$ in place of $\theta$.
$$\cot\frac{A}{2}=\frac{1}{\tan\frac{A}{2}}$$
Thus,
$$\cot\frac{A}{2}=\frac{1}{\frac{\sin A}{1+\cos A}}$$
$$\cot\frac{A}{2}=\frac{1+\cos A}{\sin A}$$
That is the identity for $\cos\frac{A}{2}$.
