Question

Precalculus only right answer please and thank you. Help me

Answer 1

Given:

`(2tanx)/(1-tan^2(x)) =√(3)`

We know the identity

`tan(2x)= (2tanx)/(1-tan^2(x))`

So we can equate
`tan(2x) =√(3)`

`tan(x) =√(3)` when
`x=(\pi)/(3)`

Tan is positive in first and third quadrant

So we will get one move value for x

`tan(x) =√(3)` when
`x=(4\pi)/(3)`

So for
`tan(2x) =√(3)`

`2x=(4\pi)/(3)` and
`2x=(\pi)/(3)`

Divide by 2 on both sides

`x=(2\pi)/(3)` and
`2x=(\pi)/(6)`

To get general solution we add
`n\pi`

So option A and option C are correct.