I assume you mean that you want to prove the following: $\lim_{\Delta x \rightarrow 0} \frac{ \sin \Delta x }{ \Delta x } = 1$ This can be done using L'Hospital's Rule or the Squeeze Theorem. http://tutorial.math.lamar.edu/Classes/CalcI/ProofTrigDeriv.aspx shows a proof using the Squeeze Theorem.