# trig reduction, where did the negative sign come from?

• October 23rd 2012, 08:01 PM
kingsolomonsgrave
trig reduction, where did the negative sign come from?
Attachment 25378

we cancel (cos x - sin x) in the numerator and denominator to get 1/(cos x)

Why is it -1?
• October 23rd 2012, 08:03 PM
MarkFL
Re: trig reduction, where did the negative sign come from?
$\cos(x)-\sin(x)=-(\sin(x)-\cos(x))$

Then after dividing out this factor, the -1 is left in the numerator.
• October 23rd 2012, 08:05 PM
TheEmptySet
Re: trig reduction, where did the negative sign come from?
Quote:

Originally Posted by kingsolomonsgrave
Attachment 25378

we cancel (cos x - sin x) in the numerator and denominator to get 1/(cos x)

Why is it -1?

Algebra Just factor a -1 out of the numerator

$\frac{a-b}{b-a}=\frac{-1(b-a)}{(b-a)}=-1$