text: Others have aswered it correctly why do it if I cannot provide a neater solution\n\nwhy disturb the second term of LHS as it has 1/sin x which is csc x\n\nnow convert the 1st term\n\n(sin x)/(1+ cos x)\n\nif we multiply and devide by (1-cos x) then denominator becomes 1- cos^2x = sin^2 x\n\nso expression 1st term = sin x(1-cos x)/sin^2 x = (1- cos x)/sin x\n\nso add the 2 to get LHS = (1-cos x)/sin x + (1+ cos x)/sin x\n= (1-cos x +1 + cos x)/sin x = 2/sin x = 2 csc x\n\nIs it not neater