If f(x)=`(tan(pi/4-x))/(cot2x) ` for `x!=pi/4,` find the value of which can be assigned to f(x) at `x=pi/4` so that the function f(x) becomes continuous every where in `[0,pi/2]`

Explanation

To find the value that can be assigned to \( f(x) \) at \( x = \frac{\pi}{4} \) so that the function becomes continuous everywhere in the interval \([0, \frac{\pi}{2}]\), we need to evaluate the limit of \( f(x) \) as \( x \) approaches \( \frac{\pi}{4} \).

### Step-by-Step Solution:

1. **Write the function**:
\[ f(x) = \frac{\tan\left(\frac{\pi}{4} - x\right)}{\cot(2x)} \quad \text{for } x \neq \frac{\pi}{4} \]
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