JEE Math Practice Question

Let $$f(x) = {{1 - \tan x} \over {4x - \pi }}$$, $$x \ne {\pi \over 4}$$, $$x \in \left[ {0,{\pi \over 2}} \right]$$. If $$f(x)$$ is continuous in $$\left[ {0,{\pi \over 2}} \right]$$, then $$f\left( {{\pi \over 4}} \right)$$ is

1. A.$$-1$$
2. B.$${1 \over 2}$$
3. C.$$-{1 \over 2}$$
4. D.$$1$$