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 [JEE Main 2025, 8 Apr (Shift 1)]

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The value of \({\cot }^{-1}\left(\frac{\sqrt{1+{\tan }^{2}(2)}-1}{\tan (2)}\right)-{\cot }^{-1}\) \(\left(\frac{\sqrt{1+…

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