`sin^4(x)cos^2(x)` Use the power reducing formulas to rewrite the expression in terms of the first power of the cosine.

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

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

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

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

`sin^4 (2x)*cos^2 x= (1 - 2cos 4x + (1 + cos 8x)/2)/4*(1 + cos 2x)/2`

`sin^4 (2x)*cos^2 x= (2 - 4cos 4x + 1 + cos 8x)/8*(1 + cos 2x)/2`

`sin^4 (2x)*cos^2 x = (3 - 4cos 4x + cos 8x)/8*(1 + cos 2x)/2`

Hence, using the power reducing formulas yields `sin^4 (2x)*cos^2 x = (3 - 4cos 4x + cos 8x)/8*(1 + cos 2x)/2`
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