Simplify tan(a/2)

Problem

tan(a/2)

Solution

1. Identify the half-angle identity for the tangent function.

2. Recall the primary identity involving sine and cosine:

tan(a/2)=(1−cos(a))/sin(a)

3. Recall the alternative identity involving sine and cosine:

tan(a/2)=sin(a)/(1+cos(a))

4. Recall the identity involving the square root:

tan(a/2)=±√(,(1−cos(a))/(1+cos(a)))

Final Answer

tan(a/2)=(1−cos(a))/sin(a)

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