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

Question

7252 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-10T15:26:52

#1/128(3-4cos(2x)+cos(4x))#

Use #sin 2A=2sin A cos A#,

#sin^2A=1/2(1-cos 2A) and cos^2A=1/2(1+cos 2A)#

#sin^4xcos^4x#

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

#=1/16(1/2(1-cos2x))^2#

#=1/64(1-2cos(2x)+cos^2(2x))#

#=1/64(1-2cos(2x)+1/2(1+cos(4x)))#

#=1/128(3-4cos(2x)+cos(4x))#