Friday, October 25, 2013

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

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