I'm just a little confused on how they factored the numerator in this step:

Where did the 1 come from?

Thank you :)

Guest Feb 22, 2019

#1**0 **

I am not sure which 1 you are referring to, but....

\(\frac{sinxcosx-sinx}{cos^2x-1}\\~\\ \qquad \text{Factorise the top}\\~\\= \frac{-sinx(-cosx+1)}{cos^2x-1}\\~\\ \qquad Sin^2x+cos^2x=1 \qquad so\\~\\ =\frac{-sinx(1-cosx)}{-sin^2x}\\~\\ \qquad \text{cancel}\\~\\ =\frac{1-cosx}{sinx}\\~\\\)

.Melody Feb 22, 2019