I want to show that g(x) returns the same value independent of x and hence is a constant.
$$g(x) = \lim_{n \rightarrow \infty}(\underbrace{f \circ f \circ \cdots \circ f}_{n\text{ times}})(x)$$
where $f = \cos \circ \tan \circ \sin$
How do I formally prove this?