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The Wikipedia article "Trigonometric identities" lists the following identity (in which I am simply changing variables):

cos a sin b = (1/2)[sin(a+b) - sin(a-b)]

Here, since the two angles are the same, this simplifies to:

cos a sin a = (1/2)[sin(2a) - sin(0)]

= (1/2)sin(2a)

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