trigonometric identities: cos2x=cos^2x-sin^2x... now, why is cos^2x-sin^2x is used?

[ken_165]

in the equation, it says that: cos2x=cos^2x-sin^2x... now, why is cos^2x-sin^2x is used?

 

[tkhunny]

in the equation, it says that: cos2x=cos^2x-sin^2x... now, why is cos^2x-sin^2x is used?

?? It's an identity. Use it when necessary. There are three versions of \(\displaystyle \cos(2x)\). Learn to use all three.

You can derive this one by yourself with this identity \(\displaystyle \cos(A+B) = \cos(A)\cos(B) - \sin(A)\sin(B)\)

Like this: \(\displaystyle \cos(2x) = \cos(x+x) =\cos(x)\cos(x) - \sin(x)\sin(x) = \cos^{2}(x) - \sin^{2}(x)\)

 

[Dr.Peterson]

in the equation, it says that: cos2x=cos^2x-sin^2x... now, why is cos^2x-sin^2x is used?

Well, it's used because it's true that cos(2x) = cos^2(x) - sin^2(x).

"Why" can mean a lot of different things. Are you looking for a proof, or for a reason to choose that form over the two other forms of the identity (2cos²x - 1 and 1 - 2sin²x), or something else?

 

[ken_165]

trigonometric identities

now the continuation, cos2x=cos^2x-sin^2x
=2cos^2x-1/... why is 2cos^2x-1 is used?