Question

How do you find the general solutions for `sinx = √(3)*cosx`?

Answer 1

`x= pi/3+kpi; k in ZZ`

Explanation:

If you divide both sides of the equation by `cosx`, you get

`tan x=sqrt(3)`

Before you do the division you have to exclude zeos of `cosx` function from the domain of the equation:

`D=RR-{pi/2+k pi, k in ZZ}` (1)

This equation has solutions in set given by:

`x= pi/3+kpi; k in ZZ` (2)

, because `tan (pi/3)=sqrt(3)` and `tan` function has a period of `pi`

All points described in (2) are in the domain (1) , so finally the answer is:

`x= pi/3+kpi; k in ZZ`