The value of $\cot ^{-1}\left(\frac{\sqrt{1+\tan ^2(2)}-1}{\tan (2)}\right)-\cot ^{-1}\left(\frac{\sqrt{1+\tan ^2\left(\frac{1}{2}\right)}+1}{\tan \left(\frac{1}{2}\right)}\right)$ is equal to
- A$\pi-\frac{5}{4}$
- B$\pi-\frac{3}{2}$
- C$\pi+\frac{3}{2}$
- D$\pi+\frac{5}{2}$
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