[math-fun] equality

Hello I still did not notice this equality between sinus functions, I find it harmonious sin(3*x)/(1-cos(3*x))=(cos(3*x)+cos(2*x)+cos(x)+1)/(sin(3*x)+sin(2*x)+sin(x)); sin(5*x)/(1-cos(5*x))=(cos(5*x)+cos(4*x)+cos(3*x)+cos(2*x)+cos(x)+1)/(sin(5*x)+sin(4*x)+sin(3*x)+sin(2*x)+sin(x)); sin(11*x)/(1-cos(11*x))=(cos(11*x)+cos(10*x)+cos(9*x)+cos(8*x)+cos(7*x)+cos(6*x)+cos(5*x)+cos(4*x)+cos(3*x)+cos(2*x)+cos(x)+1)/(sin(11*x)+sin(10*x)+sin(9*x)+sin(8*x)+sin(7*x)+sin(6*x)+sin(5*x)+sin(4*x)+sin(3*x)+sin(2*x)+sin(x)); general sin(k*x)/(1-cos(k*x))=(sum(cos(n*x),n=0..k))*(sum(sin(n*x),n=0..k))^(-1);