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

This is the expression for angle between two lines

This expression will change its sign depending upon whether we take 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

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