Prove that \( \cos \tan ^{-1}\left[\sin \left(\cot ^{-1} x\right)\r...

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Prove that \( \cos \tan ^{-1}\left[\sin \left(\cot ^{-1} x\right)\right]=\sqrt{\frac{x^{2}+1}{x^{2}+2}} \).(2002, 5M)
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