How do you prove #sin^4 X = (cos^2 2X - 2 cos 2x + 1) / 4#?

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Answer 1 · 2016-04-30T00:58:47

Using the following:

we have:

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

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

#=(-2sin^2(x))^2/4#

#=(4sin^4(x))/4#

#=sin^4(x)#