Original
We proved continuity of polynomials earlier using the Sum Law, Product
Law and continuity of power functions.
We proved continuity of rational functions earlier using the Quotient
Law and continuity of polynomials.
We can prove continuity of the remaining four trig functions using the
Quotient Law and continuity of sine and cosine functions.
Since a continuous function and its inverse have ``unbroken'' graphs,
it follows that an inverse of a continuous function is continuous on
its domain.
This implies that inverse trig functions are continuous on their domains.
Using the Limit Laws we can prove that given two functions, both
continuous on the same interval, then their sum, difference, product,
and quotient (where defined) are also continuous on the same interval
(where defined).
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