Question

Trig. Identities: Solve from one side only please to prove it
cos(3x) = 4 cos^3 x - 3 cos x

Answer 1

ok cos(3x) = cos(2x+x)
using angle addition identity
cos(2x+x) = cos(2x)cos(x) - sin(2x)sin(x)
...
using double angle identities
cos(2x) = 2cos(x)^2 - 1
sin(2x) = 2sin(x)cos(x)
...
= (2cos(x)^2 - 1)*cos(x) - (2sin(x)cos(x))*sin(x)
=2cos(x)^3 - cos(x) - 2cos(x)sin(x)^2
...
using trig identity
sin(x)^2 = 1-cos(x)^2
...
=2cos(x)^3-cos(x)-2cos(x)(1-cos(x)^2)
=4cos(x)^3 - 3cos(x)

Answer 2

hope you can follow that

Answer 3

Yes, that is sooooo helpful! Thanks a bunch, I was really stuck!

Answer 4

your welcome, its really just knowing which identies to use you to play around with it a little bit