Find the combined equation of the lines passing through the origin and having inclinations `(pi)/(3) and (5 pi)/(3).`

Explanation

Slope of the line having inclinations `theta` is `tan theta`.
Inclinations of the given lines are `(pi)/(3) and (5pi)/(3)`.
`therefore` their slopes are `m_(1) = tan ""(pi)/(3) = sqrt(3)` and
`m_(2) = tan""(5pi)/(3) = tan(2pi -(pi)/(3)) =-tan (pi)/(3) = -sqrt(3)`.
SInce the lines pass through the origin, their equations are
`y = sqrt(3)x and y = -sqrt(3)x`
i.e., `sqrt(3)x - y = 0 and sqrt(3)x + y = 0`
`therefore` the joint equation of these lines is `(sqrt(3)-y)(sqrt(3)x + y) = 0`
`therefore 3x^(2) - y^(2) = 0`.