How do you prove that # 2cos^4x + 2sin^2xcos^2x = cos2x + sin^2x+cos^2x #?

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Answer 1 · 2018-07-15T04:15:24

Here #cos^2x + sin^2x = 1#

The question provided by you now can be written as:-

#2cos x + 2 sin ^2x cos^2 x = cos 2 x +1#

#=># #2 cos^4x + 2sin^2xcos^2x#

#=># Now taking #2cos^2 x# common we get,

#=># #2cos^x (cos^2x+sin^2x)#

#=># Now this equation becomes, #2cos^2x#

#=># This can be written as:- #cos 2x +1#