Using mean value theorem, prove that `tanx > x` for all `x(0,pi/2)dot`

Explanation

To prove that \( \tan x > x \) for all \( x \in (0, \frac{\pi}{2}) \) using the Mean Value Theorem, we can follow these steps:

### Step 1: Define the function
Let \( f(x) = \tan x - x \). We want to show that \( f(x) > 0 \) for all \( x \in (0, \frac{\pi}{2}) \).

### Step 2: Check continuity and differentiability
The function \( f(x) \) is continuous on the interval \( [0, \frac{\pi}{2}) \) and differentiable on \( (0, \frac{\pi}{2}) \) because \( \tan x \) is continuous and differentiable in this interval.

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