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

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

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

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

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

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

Hence, eusing the power reducing formulas...

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

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

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

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

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

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

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

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