The area of the region above the x - axis bounded by the curve $\;y=tan x\;,0 \leq x \leq \large\frac{\pi}{2}\;$ and the tangent to the curve at $\;x= \large\frac{\pi}{4}\;$ is :

Question

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