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Question

If $ A = \frac{1}{\pi}\left[\sin^{-1}(\pi x) + \tan^{-1}\left(\frac{x}{\pi}\right) + \cot^{-1}(\pi x)\right]$, $ B = \frac{1}{\pi}\left[-\cos^{-1}(\pi x) + \sin^{-1}\left(\frac{x}{\pi}\right) - \tan^{-1}(\pi x)\right]$, then $ A - B $ is equal to:

$ I $

$ 0 $

$ 2I $

$ \frac{1}{2}I $

Solution

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