SOLUTION: Find an equivalent expression for cos 3x in terms of powers of cos x. cos 3x = cos (2x + x) = cos 2x cos x - sin 2x sin x <----Using cos(u + v) = cos u cos v - s

Algebra ->  Trigonometry-basics -> SOLUTION: Find an equivalent expression for cos 3x in terms of powers of cos x. cos 3x = cos (2x + x) = cos 2x cos x - sin 2x sin x <----Using cos(u + v) = cos u cos v - s      Log On


   

Question 285156: Find an equivalent expression for cos 3x in terms of powers of cos x.
cos 3x = cos (2x + x)
= cos 2x cos x - sin 2x sin x <----Using cos(u + v) = cos u cos v - sin u sin v
= (cos^2x - sin^2x) cosx - (2 sinx cosx) sinx
= cos^3x -sin^2x cosx - 2sin^2x cosx
I'm stuck up to here....

Answer by eggsarecool(46) About Me  (Show Source):
You can put this solution on YOUR website!
Going back to this step (cos^2x - sin^2x) cosx - (2 sinx cosx) sinx
You need to use identities 1-%28cos%28x%29%29%5E2=%28sin%28x%29%29%5E2
So %28cos%28x%29%29%5E2-%281-%28cos%28x%29%29%5E2%29-2%28sin%28x%29%29%5E2%2Acos%28x%29
Simplify.
%28cos%28x%29%29%5E2-1%2B%28cos%28x%29%29%5E2-2%281-%28cos%28x%29%29%5E2%29%2Acos%28x%29
2%28cos%28x%29%29%5E2-1-2%28cos%28x%29-%28cos%28x%29%29%5E3%29 And everything is now in terms of cos%28x%29 powers.