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First we look at the double-angle identity of cos2x.

We know that:

cos2x = cos^2x - sin^2x

cos2x = [1-sin^2x] - sin^2x.............. (From sin^2x + cos^2x = 1, cos^2x = 1 - sin^2x)

Therefore:

cos2x = 1 - 2sin^2x

2sin^2x = 1 - cos2x

sin^2x = 1/2(1-cos2x)

sin^2x = 1/2 - cos2x/2

And intergrating, we get:

x/2 - sin2x/4 + c...................(Integral of cos2x = 1/2sin2x; and c is a constant)

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โˆ™ 2012-08-10 03:06:52
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