Question

How do I solve `cot^2 theta +sqrt3 cot theta = 0`?

Answer 1

`theta=pmpi/2+2kpi`,`theta_1=-pi/6+2kpi,theta_2=5pi/6+2kpi`

Explanation:

Rewriting your equation in the form
`cot(theta)(cot(theta)+sqrt(3))=0`
so we get two cases:

`cot(theta)=0`
since

`cot(x)=cos(x)/sin(x)=0`if `cos(x)=0`

we get

`theta=pmpi/2+2kpi`
the other case:
`cot(theta)=-sqrt(3)`
`theta_1=-pi/6+2kpi`
`theta_2=(5pi)/6+2kpi`