If `f(x)=(tan(pi/4-x))/(cot2x)` for `x!=pi/4,` find the value 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]dot`

Explanation

If `f(x)` is continuous at `x=frac{pi}{4}`



`lim _{x -> frac{pi}{4}} f(x)=f(frac{pi}{4}) `


`Rightarrow lim _{x -> frac{pi}{4}} frac{tan (frac{pi}{4}-x)}{cot 2 x}=f(frac{pi}{4})`



If `frac{pi}{4}-x=y`, then



`x -> frac{pi}{4} text { and } y -> 0`


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