Question

Find all solutions of the equation in the interval [0, 2)

Answer 1

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

Explanation:

sin²x = 3cos²x

`(sin^2 x)/(cos^2 x)` = 3

tan²x = 3, x ∈ [0, 2π)

tan x = √3 , x ∈ [0, 2π)

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