Please help me to solve this, use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles. #sin^4(5x) cos^2(5x)#?

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Answer 1 · 2018-06-15T03:56:35

#sin^4(5x) cos^2(5x)#

#=1/2(2sin^2(5x))*1/4(2sin(5x) cos(5x))^2#

#=1/8(2sin^2(5x))(2sin(5x) cos(5x))^2#

#=1/8(1-cos(10x))*sin^2(10x)#

#=1/16(1-cos(10x))*2sin^2(10x)#

#=1/16(1-cos(10x))*(1-cos(20x))#
#=1/16(1-cos(10x)-cos(20x)+cos(10x)cos(20x))#

#=1/16(1-cos(10x)-cos(20x)+1/2(cos(15x)+cos(5x)))#

#=1/32(2-2cos(10x)-2cos(20x)+cos(15x)+cos(5x))#