Question

use the limit process to prove the derivative of the sine function.


use the quotient rule to prove the derivative of the tangent function.

Answer 1

For this you need:

\[\large \lim_{\theta\rightarrow0} {\frac{\cos\theta - 1}{\theta}} = 0\]

Answer 2

I use that for the sine function?

Answer 3

Set up your difference quotient and see if you don't.

Answer 4

You do also need

\[ \large \lim_{\theta\rightarrow0} {\sin\theta \over \theta} = 1 \]


Since one of these can be derived of the other, the proof of them is generally offered before trig derivatives.