reserve th, th1, th2, th3 for Real;

theorem
  (sin(th1)+sin(th2))/(sin(th1)-sin(th2)) = tan((th1+th2)/2)*cot((th1- th2)/2 )
proof
  (sin(th1)+sin(th2))/(sin(th1)-sin(th2)) = 2*(cos((th1-th2)/2)*sin((th1+
  th2)/2))/(sin(th1)-sin(th2)) by Th15
    .= 2*(cos((th1-th2)/2)*sin((th1+th2)/2)) /(2*(cos((th1+th2)/2)*sin((th1-
  th2)/2))) by Th16
    .= (2/2)*((cos((th1-th2)/2)*sin((th1+th2)/2)) /(cos((th1+th2)/2)*sin((
  th1-th2)/2))) by XCMPLX_1:76
    .= tan((th1+th2)/2)*cot((th1-th2)/2) by XCMPLX_1:76;
  hence thesis;
end;
