Why don't the secants cancel in this equation?

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The discussion centers on confusion regarding the cancellation of secants in a mathematical equation. The user initially believes that the positive and negative secants should cancel each other out but realizes this is not the case. They express understanding of tangent manipulations but seek clarity on the transition between steps in the equation. The user concludes that expanding the numerator and factoring out sec x is the correct approach. Overall, the focus is on understanding the algebraic manipulations involved in the equation.
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Homework Statement



Screenshot2012-01-25at35053AM.png


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
 
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its simple. just expand the numerator and then take sec x common
 
ok, I get it

ab - ac = a(b-c)
 

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