sin(2x)=2sin(x)cos(x); cos(2x)=2cos2(x)-1.
(sin(2x)-sin(x))/(cos(2x)+cos(x))=(2sin(x)cos(x)-sin(x))/(2cos2(x)-1+cos(x)),
(sin(2x)-sin(x))/(cos(2x)+cos(x))=sin(x)(2cos(x)-1)/((2cos(x)-1)(cos(x)+1)),
(sin(2x)-sin(x))/(cos(2x)+cos(x))=sin(x)/(1+cos(x)) QED