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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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