Can u tell me how can cos 3x = 4cos³x-3cos x?

Question

1590 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-12T14:24:25

I tried this:

Have a look:
enter image source here

Answer 2 · 2017-07-12T14:28:40

See the proof below

We need

#sin^2x+cos^2x=1#

#sin2x=2sinxcosx#

#cos2x=2cos^2x-1#

#cos(a+b)=cosacosb-sinasinb#

#LHS=cos 3x= cos(2x+x)#

#=cos2xcosx-sin2xsinx#

#=(2cos^2x-1)cosx-2sinxcosxsinx#

#=2cos^3x-cosx-2cosxsin^2x#

#=2cos^3x-cosx-2cosx(1-cos^2x)#

#=2cos^3x-cosx-2cosx+2cos^3x#

#=4cos^3x-3cosx#

#=RHS#

#QED#