Prove that the function defined by `f(x) = t a n x`is a continuous function.

Explanation

To prove that the function \( f(x) = \tan x \) is continuous in the interval \( (0, 90^\circ) \), we will follow these steps:

### Step 1: Understand the Definition of Continuity
A function \( f(x) \) is continuous at a point \( c \) if:
1. \( f(c) \) is defined.
2. \( \lim_{x \to c} f(x) \) exists.
3. \( \lim_{x \to c} f(x) = f(c) \).

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