Simplify cos(a/2)

Problem

cos(a/2)

Solution

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

2. Apply the formula for the cosine of a half-angle, which relates cos(a/2) to cos(a)

3. Determine the sign based on the quadrant in which the angle a/2 resides. Since the quadrant is not specified, the result includes a ± symbol.

Final Answer

cos(a/2)=±√(,(1+cos(a))/2)

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