The value of \( \cot ^{-1}(21)+\cot ^{-1}(13)+\cot ^{-1}(-8) \) is
\(\cot^{-1}21 + \cot^{-1}13 = \tan^{-1}\frac{1}{21} + \tan^{-1}\frac{1}{13} = \tan^{-1}\frac{\frac{34}{273}}{1 - \frac{1}{273}} = \tan^{-1}\frac{1}{8}\)
\(\cot^{-1}(-8) = \pi - \cot^{-1}8 = \pi - \tan^{-1}\frac{1}{8}\)
Sum = \(\pi\)
Answer: (B) π
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