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 Skip Navigation LinksMath Help > Trigonometry > Trig Equivalences > sin (x/2) cos (x/2) = (1/2) sin x

sin (x/2) cos (x/2) = (1/2) sin x

Why is this true?  Here's a most beautiful geometric proof:

Here are two identical isosceles triangles.  The one on the left has a base of 2 sin(x/2) and a height of cos(x/2).  The one on the right has a base of 1 and a height of sin x.

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