How do you prove #2 cos^2 A - 1 = cos(2A)#?

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Answer 1 · 2016-03-14T01:06:16

Well we know that for two angles #A,B# it holds that

#cos(A+B)=cosAcosB-sinA*sinB#

hence for #A=B# you get

#cos(2A)=cos^2A-sin^2A#

But #sin^2A=1-cos^2A#

hence

#cos(2A)=cos^2A-(1-cos^2A)=2cos^2A-1#