How would you use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine? cos^4(x)sin^4(x)

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Answer 1 · 2018-02-28T06:48:26

#rarrcos^4x*sin^4x=1/128[3-4cos4x+cos8x]#

#rarrcos^4x*sin^4x#

#=1/16[(2sinx*cosx)^4]#

#=1/16[sin^4(2x)]#

#=1/64[(2sin^2(2x)]^2#

#=1/64[1-cos4x]^2#

#=1/64[1-2cos4x+cos^2(4x)]#

#=1/128[2-4cos4x+2cos^2(4x)]#

#=1/128[2-4cos4x+1+cos8x]#

#=1/128[3-4cos4x+cos8x]#