While answering this question I have used that \begin{equation}\sin x=\displaystyle\sum_{n=0}^\infty\dfrac{(-1)^nx^{2n+1}}{(2n+1)!}\end{equation} Nwe my question is that how can it be shown that the definition of $\sin x$ using the notion of perpendiculars and hypotenuse is equivalent to this definition?
As has been standard to proving that $A$ and $B$ are equivalent one first needs to show that $A \implies B$ and then $A \impliedby B$. I thought about applying this for sometime but in either case I am lost. Any ideas?
Note:- I have also read this question but the answer seemed to me to be circular. So, even if the question is almost similar to the previously linked question, I posted it as a different question because my requirements are different.
