If $f(x)=\large\frac{1-\tan x}{4x-\pi}\qquad $$x\neq \large\frac{\pi}{4}$,$x \in [0,\large\frac{\pi}{2}]$ and f(x) is continuous in $[0,\large\frac{\pi}{2}]$ then $f(\large\frac{\pi}{4})$

Question

$(a)\;1\qquad(b)\;\large\frac{1}{2}$$\qquad(c)\;-\large\frac{1}{2}$$\qquad(d)\;-1$