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

Question

35361 views around the world

You can reuse this answer
Creative Commons License

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

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

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