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 = (\cos x-1)/(\sin x) + (\sin x)/(\cos x+1) = ((\cos x-1)(\cos x+1)+sin^2x)/(sin x(\cos x+1))= \\\;\\ \\\;\\ = (\cos ^2x - 1 +sin^2x)/(sin x(\cos x+1))= (\cos ^2x +sin^2x -1)/(sin x(\cos x+1))= ( 1- 1 )/(sin x(\cos x+1))= 0`