SOLUTION: Prove sin(4x)=8sin(x)cos^3(x)-4sin(x)cos(x)

Algebra ->  Geometry-proofs -> SOLUTION: Prove sin(4x)=8sin(x)cos^3(x)-4sin(x)cos(x)      Log On


   

Question 1151813: Prove
sin(4x)=8sin(x)cos^3(x)-4sin(x)cos(x)
Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!
We use two identities

     sin%282theta%29=2sin%28theta%29cos%28theta%29
and
     cos%28theta%29=2cos%5E2%28theta%29-1

to prove:

sin%284x%29=8sin%28x%29cos%5E3%28x%29-4sin%28x%29cos%28x%29

Begin with the left side:

sin%284x%29

sin%282%282x%29%5E%22%22%29

2sin%282x%29cos%282x%29

2%282sin%28x%29cos%28x%29%5E%22%22%29%282cos%5E2%28x%29%5E%22%22-1%29

4sin%28x%29cos%28x%29%282cos%5E2%28x%29%5E%22%22-1%29

8sin%28x%29cos%5E3%28x%29-4sin%28x%29cos%28x%29

Edwin