For ` x in (0,(pi)/(2))` prove that `"sin"^(2) x lt x^(2) lt " tan"^(2) x`

Explanation

To prove that \( \sin^2 x < x^2 < \tan^2 x \) for \( x \in \left(0, \frac{\pi}{2}\right) \), we will break this proof into two parts:

1. Proving \( \sin^2 x < x^2 \)
2. Proving \( x^2 < \tan^2 x \)

### Step 1: Proving \( \sin^2 x < x^2 \)

**Let \( f(x) = \sin^2 x - x^2 \)**
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