text: (sinx / 1 + cosx) + (1 + cosx / sinx) = 2cscx? prove this identity others have aswered it correctly why do it if i cannot provide a neater solution  why disturb the second term of lhs as it has 1/sin x which is csc x  now convert the 1st term  (sin x)/(1+ cos x)  if we multiply and devide by (1-cos x) then denominator becomes 1- cos^2x = sin^2 x  so expression 1st term = sin x(1-cos x)/sin^2 x = (1- cos x)/sin x  so add the 2 to get lhs = (1-cos x)/sin x + (1+ cos x)/sin x = (1-cos x +1 + cos x)/sin x = 2/sin x = 2 csc x  is it not neater