SOLUTION: prove the following identity: cos2A = 2cos^2A - 1

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Question 32478: prove the following identity:
cos2A = 2cos^2A - 1
Answer by sarah_adam(201) About Me  (Show Source):
You can put this solution on YOUR website!
Cos2A = Cos(A+A)
we know the formula for Cos(A+B)=CosACosB-SinASinB
therefore Cos(A+A)= CosACosA - SinASinA
= Cos^2A - Sin^2A
WE also know that Cos^2A + Sin^2A = 1
therfore Sin^2A = 1 - Cos^2A
Replacing the value of Sin^2A
Cos(A+A)= Cos^2A - (1 - Cos^2A)
Cos2A = Cos^2A - 1 +Cos^2A
Hence Cos2A = 2Cos^2A - 1
Thus Proved.