`cos(2x) - cos(x) = 0` Find the exact solutions of the equation in the interval [0, 2pi).

Expert Answers
gsarora17 eNotes educator| Certified Educator

`cos(2x)-cos(x)=0 , 0<=x<=2pi`

using the identity `cos(2x)=2cos^2(x)-1`



Let cos(x)=y,


solving using the quadratic formula,



`:. cos(x)=1, cos(x)=-1/2`


General solutions are,

`x=(2pi)/3+2pin, x=(4pi)/3+2pin`

Solutions for the range `0<=x<=2pi` are,

`x=(2pi)/3 , x=(4pi)/3`


General solutions are,


solutions for the range `0<=x<=2pi`  are,

`x=0 , x=2pi`

combine all the solutions ,

`x=0, x=2pi , x=(2pi)/3 , x=(4pi)/3`