Prove that `[lim_(xrarr0) (sinx.tanx)/(x^(2))]=1`,where [.] represents greatest integer function.

Explanation

To prove that \(\left[\lim_{x \to 0} \frac{\sin x \tan x}{x^2}\right] = 1\), where \([.]\) denotes the greatest integer function, we will follow these steps:

### Step 1: Rewrite the limit expression
We start with the limit:
\[ \lim_{x \to 0} \frac{\sin x \tan x}{x^2} \]
We can rewrite \(\tan x\) as \(\frac{\sin x}{\cos x}\):
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