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There are formulae like sinA+SinB=2sin(A+B/2)cos(A-B/2) and cosA-cosB=-2sin(A+B/2)sin(A-B/2).With the help of these we can write,
sinA+sin2A=2sin(3A/2)cosA/2 and cosA-cos2A=-2sin(3A/2)sin(-A/2).Therefore 2sin(3A/2) will be canceled out and (cosA/2)/sin(A/2)=cot(A/2).
I hope that you have understood.
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