Very Carefully…

The top portion of this fraction is a difference of 2 squares, meaning

##sin^2(x)-cos^2(x)=(sin(x)+cos(x))(sin(x)-cos(x))##, so

##(sin^2(x)-cos^2(x))/(sin(x)+cos(x))=((sin(x)+cos(x))(sin(x)-cos(x)))/(sin(x)+cos(x))##

##=sin(x)-cos(x)##

Very Carefully…

The top portion of this fraction is a difference of 2 squares, meaning

##sin^2(x)-cos^2(x)=(sin(x)+cos(x))(sin(x)-cos(x))##, so

##(sin^2(x)-cos^2(x))/(sin(x)+cos(x))=((sin(x)+cos(x))(sin(x)-cos(x)))/(sin(x)+cos(x))##

##=sin(x)-cos(x)##