Question

Solve the equation `cos2x-cosx=0`?

Answer 1

`x=(2n+1)pi` or `x=2npi+-(2pi)/3`, where `n` is an integer

Explanation:

Using identity `cos2x=2cos^2x-1`, `cos2x-cosx=0` can be written as

`2cos^2x-cosx-1=0` and hence using quadratic formula

`cosx=(-(-1)+-sqrt((-1)^2-4xx2xx(-1)))/(2xx2)`

`=(1+-sqrt9)/4`

`=(1+-3)/4`

`=1` or `-1/2`

If `cosx=1`, `x=(2n+1)pi`, where `n` is an integer

and if `cosx=-1/2`, `x=2npi+-(2pi)/3`, where `n` is an integer