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折开来看看比较容易一些：
sin^2 x = 1/2 - (1/2) cos 2x
= (1/2) - (1/2)(1-(2x)^2/2!-...+(-1)^(n+1)(2x)^2n/(2n!)+...], n from 1 to oo
= (1/2) - (1/2) + [2x^2/2!.+(-1)^(n+1)(2)^(2n-1)x^(2n)/2n!+...], n from 1 to oo
= sum[n=1, oo] (-1)^(n+1)(2)^(2n-1)x^(2n)/2n!
sin^2 x = 1/2 - (1/2) cos 2x
= (1/2) - (1/2)(1-(2x)^2/2!-...+(-1)^(n+1)(2x)^2n/(2n!)+...], n from 1 to oo
= (1/2) - (1/2) + [2x^2/2!.+(-1)^(n+1)(2)^(2n-1)x^(2n)/2n!+...], n from 1 to oo
= sum[n=1, oo] (-1)^(n+1)(2)^(2n-1)x^(2n)/2n!
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