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

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Answer 1 · 2017-12-14T04:02:12

#(1 - 4sin^4 x) = (1 - 2sin^2 x)(1 + 2sin^2 x)#
Use trig identity:
#cos 2x = 1 - 2sin^2 x#.
We get:
#(1 - 4sin^4 x) = cos 2x(1 + 2sin^2 x)#. Proved