1. The problem statement, all variables and given/known data lim (-x + sin(sinx))/(x(-1 + cos(sinx))) x-> 0 2. Relevant equations sinθ/θ=1 as θ-> 0 Squeeze Theorem? 3. The attempt at a solution Well I've tried doing L'Hopital's rule, but to no avail. Each subsequent derivative just makes the equation nastier and more convoluted. Eg. lim d/dx(-x + sin(sinx))/d/dx(x(-1 + cos(sinx)))=-1 + cosx(cos(sinx))/(-1 + cos(sinx) - xcosx(sin(sinx)))=the next one is even longer and nothing jumps out at me for a possible solution. I've also attempted to rewrite the equation but again to no avail. I've also thought about squeeze theorem, but don't know how to apply it here. Any ideas?