Question

How do you solve `cos x - cos 2x = 0`?

Answer 1

Use the Property: `cos 2A=2cos^-2A-1`

`cosx-(2cos^2x -1)=0`

`-1 [cosx -2cos^2x+1]=0`

`2cos^2x-cosx-1=0`

`(2cosx+1)(cosx-1)=0`

`cosx=-1/2 or cos x=1`

`x=cos^-1(-1/2) or x=cos^-1 1`

`x=+- (2pi)/3 + 2pin or x=0+2pin`

`S={+- (2pi)/3 + 2pin , 0+2pin}`