`sin^2(2x)cos^2(2x)` Use the power reducing formulas to rewrite the expression in terms of the first power of the cosine.

Monday, January 25, 2010

According to the power reducing formulas, you may re-wrute the expression such that:

`sin^2(2x)*cos^2(2x) = (1 - cos2*(2x))/2*(1 + cos2*(2x))/2`

`sin^2(2x)*cos^2(2x) = ((1 - cos 4x)(1 + cos 4x))/4`

`sin^2(2x)*cos^2(2x) = (1 - cos^2 4x)/4`

`sin^2(2x)*cos^2(2x) = (sin^2 4x)/4`

`sin^2(2x)*cos^2(2x) = ((1 - cos2*(4x))/2)/4`

`sin^2(2x)*cos^2(2x) = (1 - cos 8x)/8`

Hence, eusing the power reducing formulas yields `sin^2(2x)*cos^2(2x) = (1 - cos 8x)/8.`

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