1. The problem statement, all variables and given/known data x in the following is actually Theta Limit as x -> 0 (cos(x) - 1) / sin(x) 2. Relevant equations none 3. The attempt at a solution Multiply both sides by cos x +1 [ (cos x - 1) / sin x ] * [ (cos x + 1 )/ (cos x + 1)] = [ cos2 x -1 ] / sin(x) (cos(x) +1) = -sin2 x / sin x (cos x + 1) - sin x / sin x cancels to -1 leaving sin x / (cos x + 1) Sub in x -> 0 = (-1) (sin(0) / cos(0) + 1) = (-1) (0/2) = 0 The only step I am not sure about the is cancelation of sin x /sin x. Is this allowed? How does the solution look?