Please help me understand how to solve Algebraically. Anybody who enters and helps me in this thread gets a 10!

[SuperGroove]

Prove Algebraically:

cos3X=4cos^3 X-3cosX

here's the steps to get to the answer, but I don't get it:

cos(2X+X)
cos2X x cosX-sin2XsinX (where did he come up with sin2XsinX?)
(cos^2 X - sin^2 X)(cosX)-(2sinXcosX)(sinX)
(cos^2 X-(1-cos2 X))(cosX)-(2sin^2 XcosX)
(cos^2 X -1+cos^2 X)(cosX)-(2cosX-2Cos^3 X)
2cos^3 X-cosX-2cosX+2cos^3 X
4cos^3 X-3cosX = 4cos^3 X-3cosX


I'm really bad at proving this stuff algebraically, and the person who I called for help wasn't home, because she was at another person's house trying to get help as well.


PLEASE...for GROOVE! And for a 10

 

[Imported]

Oh no.. I just went through this in Pre-Cal.. I'll see what I can do..

Blah.. I hate identities. Can't do it..

 

[beer]

It's one of your identies. I don't remember more though.

 

[Azraele]

So you were given the proof and now it has to be proved using algrbra. Eek! It's been a long time since HS math, but I'll see what I can whip up.

 

[Lily27]

Its an identity cos(x+y) = cosxcosy-sinxsiny

 

[GammaRayX]

cos(2X+X)
cos2X x cosX-sin2XsinX (where did he come up with sin2XsinX?)
(cos^2 X - sin^2 X)(cosX)-(2sinXcosX)(sinX)
(cos^2 X-(1-cos2 X))(cosX)-(2sin^2 XcosX)
(cos^2 X -1+cos^2 X)(cosX)-(2cosX-2Cos^3 X)
2cos^3 X-cosX-2cosX+2cos^3 X
4cos^3 X-3cosX = 4cos^3 X-3cosX

Okay, just remeber the trigiometric angle addition formulas.
Mainly
cos(a+b) = cos(a)*cos(b) - sin(a)sin(b)
sin(a+b) = cos(a)*sin(b) + sin(a)*cos(b)

For for the special case of doubling an angle, its
cos(2x) = cos(x)*cos(x) - sin(x)*sin(x) which reduces to cos²(x) - sin²(x)
sin(2x) = 2*cos(x)*sin(x)

The whole proof is nothing more than following the angle addition formulas.

 

[Scott Newton]

Ummm Yeah.... What Gamma said.

 

[Sukhoi]

Yeah, it's an identity. I'd do it, but I hate identities, so I'm not going to.

 

[SuperGroove]

Thanks guys and gals. I can't beieve that didn't come to me! I just couldn't remember the identities for the life of me. Everyone got a ten