Why don't the secants cancel in this equation?

[bobsmith76]

Homework Statement

Homework Equations

The Attempt at a Solution

I don't see how they get from step one to two. I would think both secants would cancel since one is positive and the other is negative but that doesn't happen. i think i understand the manipulations of the tangents but not entirely

 

[issacnewton]

its simple. just expand the numerator and then take sec x common

 

[bobsmith76]

ok, I get it

ab - ac = a(b-c)