For any integer $n\geq 1$, define $\sin_n=\sin\circ ... \circ \sin$ ($n$ times). Prove that $\lim_{x\to 0}\frac{\sin_nx}{x}=1$ for all $n\geq 1$ I got this problem:
For any integer $n\geq 1$, define $\sin_n=\sin\circ ... \circ \sin$ ($n$ times). Prove that $\lim_{x\to 0}\frac{\sin_nx}{x}=1$ for all $n\geq 1$.
Some hints will be appreciated.

Hint : multiply and divide by $\sin_{n-1}x$ and then try to simplify then again multiply and divide by $\sin_{n-2} x$ and now I think you can carry out from here
