Question

Simplify the expression: (cosx-1)/sinx + sinx/(cosx +1) ?? I got cosx but the answer is zero?? Je ne sais quoi!!! Btw the question is the top one! Thanks!!!!

Answer 1

(cosx-1)/sinx + sinx/(cosx +1) =?


$\it E = \dfrac{\cos x-1}{\sin x} + \dfrac{\sin x}{\cos x+1} = \dfrac{(\cos x-1)(\cos x+1)+sin^2x}{sin x(\cos x+1)}= \\\;\\ \\\;\\ = \dfrac{\cos ^2x - 1 +sin^2x}{sin x(\cos x+1)}= \dfrac{\cos ^2x +sin^2x -1}{sin x(\cos x+1)}= \dfrac{ 1- 1 }{sin x(\cos x+1)}= 0$