Question

How do you solve `cosx=3cosx+1`?

Answer 1

`x=2kpi+-2pi/3, k in ZZ`.

Explanation:

`cosx=3cosx+1`

`rArr -2cosx=1`

`rArr cosx=-1/2=-cos(pi/3)=cos(pi-pi/3)=cos2pi/3...(1)`

Now, we can use the soln. to the eqn. `costheta=cosalpha` is,

`theta=2kpi+-alpha, k in ZZ`

Using this soln. for `(1)`, we get,

`x=2kpi+-2pi/3, k in ZZ`.