the angle between the lines y =√3x+1 and y+√3x-3= 0 is
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y - √3x- 5 = 0
y= √3x+5 ( y = mx + c )
Slope m1 = √3
√3y-x+6 =0
√3y = x -6
y = x/√3–6/√3
slope m2= 1/√3
tan theta =( m1-m2)/(1+m1m2)
tan theta = (√3–1/√3)/[1+(√3*1/√3)]
tan theta = [(√3*√3–1)/√3]/ 1+1)
= [(3–1/√3)]/ 2
= (2/√3)/2
= 1/√3
tan theta = 1/√3
tan30° = 1/√3
The angle between the lines is 30°.
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