How do you use the power reducing formulas to rewrite the expression #sin^4xcos^2x# in terms of the first power of cosine?

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Answer 1 · 2017-01-03T08:58:57

#sin^4xcos^2x=1/8(3+cos4x-4cos2x)(1+cos2x)#

To rewrite #sin^4xcos^2x# in terms of the first power of cosine, we use identities

#cos2A=2cos^2A-1=1-2sin^2A#

Hence #sin^4xcos^2x#

= #(sin^2x)^2cos^2x#

= #((1-cos2x)/2)^2(1+cos2x)#

= #(1/2-(cos2x)/2)^2(1+cos2x)#

= #(1/4+(cos^2 2x)/4-(cos2x)/2)(1+cos2x)#

= #(1/4+(1+cos4x)/8-(cos2x)/2)(1+cos2x)#

= #1/8(3+cos4x-4cos2x)(1+cos2x)#