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Bro

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## Homework Statement

lim (-x + sin(sinx))/(x(-1 + cos(sinx)))

x-> 0

## Homework Equations

sinθ/θ=1 as θ-> 0

Squeeze Theorem?

## 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?