Question

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Answer 1

x =
`(4\pi )/(9),(10\pi )/(9)`

Explanation:

Given equation is,

`√(3)\text{tan}((2x)/(3))+1=0`

By solving this equation,

`\text{tan}((2x)/(3))=-(1)/(√(3))`

`x=(2)/(3)* \text{tan}^(-1)(-(1)/(√(3)))` [tangent of any angle is negative in IInd and IVth quadrants]

x =
`(2)/(3)* ((2\pi )/(3))`,
`(2)/(3)* ((5\pi)/(3))`

x =
`(4\pi )/(9),(10\pi )/(9)`

Therefore, value of x in the interval of [0, 2π] are
`(4\pi )/(9),(10\pi )/(9)`.