Let `f(x)=(tan(pi/4-x))/(cot2x),x!=pi/4` . The value which should be assigned to `f(x)` at `x=pi/4,` so that it is continuous everywhere is (a) `1` (b) `1/2` (c) 2 (d) none of these

Explanation

To find the value that should be assigned to \( f(x) \) at \( x = \frac{\pi}{4} \) for the function to be continuous everywhere, we need to evaluate the limit of \( f(x) \) as \( x \) approaches \( \frac{\pi}{4} \).

### Step-by-Step Solution:

1. **Define the Function**:
\[ f(x) = \frac{\tan\left(\frac{\pi}{4} - x\right)}{\cot(2x)}, \quad x \neq \frac{\pi}{4} \]
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