Question

How do you solve `cos 2θ + cosθ = 0` from `[0,2pi]`?

Answer 1

`theta=pi/3 vv theta=(5pi)/3 vv theta=pi`

Explanation:

`cos2theta=cos^2theta-sin^2theta`
`cos^2theta-sin^2theta+costheta=0`
`sin^2theta+cos^2theta=1 => sin^2theta=1-cos^2theta`
`cos^2theta-(1-cos^2theta)+costheta=0`
`cos^2theta-1+cos^2theta+costheta=0`
`2cos^2theta+costheta-1=0`
`2cos^2theta-costheta+2costheta-1=0`
`costheta(2costheta-1)+2costheta-1=0`
`(2costheta-1)(costheta+1)=0`
`2costheta-1=0 vv costheta+1=0`
`costheta=1/2 vv costheta=-1`
`theta=pi/3 vv theta=(5pi)/3 vv theta=pi`