Question

3cot^(2 )x-1=0

Pls Help

Answer 1

`x=(\pi )/(6) ,(7\pi )/(6)`

Explanation:

`3*cot^2x-1=0\\\\3*cot^2x=1\\\\cot^2x=(1)/(3) \\\\cot(x)=\sqrt{(1)/(3) } \\\\cot(x)=(1)/(√(3) ) \\\\(1)/(tan(x))=(1)/(√(3) ) \\\\tan(x)=√(3) \\`

x=tan^-1(
`√(3)`)

It has to be in Quadrant 1
`(+)/(+) =+` or 3
`(-)/(-)=+` for positive.

`x=(\pi )/(6) ,(7\pi )/(6)`

Unless that incorrect due to tan(x) range is
`-(\pi )/(2) \leq x\leq (\pi )/(2)`. Then the only answer is
`x=(\pi )/(6)`