Integrate : $\int \limits_0^{\large\frac{\pi}{2}} min ^m \{ \tan x , \cot x \} dx$

Question

$$\begin {array} {1 1} (a)\;\log \sqrt 2 \\ (b)\;\log 2 \sqrt 2 \\ (c)\;\log(\frac{1}{2}) \\ (d)\;\log 2 \end {array}$$