why do we apply mode to tan theta= m2-m1/1+m1m2 tan theta can itself get both positive and negative - Maths - Principle of Mathematical Induction

Question

why do we apply mode to tan theta= m2-m1/1+m1m2 ? tan theta can
itself get both positive and negative values what is the use of
this modulus? not also here but it has been applied to many other
cases

Pronay · Accepted Answer

$\tan θ = \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}$

This is the expression for angle between two lines

This expression will change its sign depending upon whether we take $m_{1}$ as slope of first line or the second.

To get rid of this sign issue , we use a modulus sign on the previous expression, which will always give a positive value(or an acute angle)

Therefore the final expression looks like

$\tan θ = \frac{| m_{1} - m_{2} |}{1 + m_{1} m_{2}}$

why do we apply mode to tan theta= m2-m1/1+m1m2 ? tan theta can itself get both positive and negative values. what is the use of this modulus? not also here but it has been applied to many other cases