Factor sin(x/2)

Problem

sin(x/2)

Solution

1. Identify the expression as a trigonometric function with a half-angle argument.

2. Apply the half-angle identity for the sine function, which relates the half-angle to the cosine of the full angle.

3. Express the identity using the radical form, noting that the sign depends on the quadrant in which x/2 lies.

Final Answer

sin(x/2)=±√(,(1−cos(x))/2)

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