6. c) Use l'Hopital's rule to evaluate lim x->0 e^x - e^-x -2x / x - sin x

step 1 = e^x + e^-x -2 / 1 - cos x

step 2 = e^x - e^-x / sin x

step 3 = e^x + e^-x / cos x

step 4 = above is = to 2/1

I do not understand how 1-cosx becomes sin x, I thought it would be -sinx. Secondly, I do not understand how step 3 is equal to 2/1.