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

Given ` f(x)=\frac{\tan (\frac{\pi}{4}-x )}{\cot 2 x} `

Given function is continuous everywhere and we have to find f(x) at ` x=\frac{\pi}{4}` , we can write,


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

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


We have to make limit tending to zero.

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