Find angles between the lines `sqrt(3)x+y=1`and `x+sqrt(3)y=1`.

Explanation

First equation : `sqrt(3)x+y=1`
Its slope `m_(1)=-(sqrt(3))/(1)=-sqrt(3)`
Second equation : `x+sqrt(3)y=0`
Its slope `m_(2)=-(1)/(sqrt(3))`
If `theta` is the angle between these lines then
`tan theta=|(m_(1)-m_(2))\(1+m_(1)m_(2))|`
`=|(-sqrt(3)+(1)/(sqrt(3)))/(1+(-sqrt(3))(-(1)/(sqrt(3))))|=|(-2//sqrt(3))/(2)|=(1)/(sqrt(3))`
`implies theta=30^(@)`
`:.` Angle between lines `=30^(@)`