If ${\cot ^{ - 1}}(\alpha ) = {\cot ^{ - 1}}{\rm{2 }} + {\rm{ co}}{{\rm{t}}^{ - 1}}{\rm{8 }} + {\rm{ co}}{{\rm{t}}^{ - 1}}18 + {\cot ^{ - 1}}32 + .....$ upto 100 terms, then $\alpha $ is

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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{\cot ^{ - 1}}(\alpha ) = {\cot ^{ - 1}}\mathrm{2 } + \mathrm{ co}{\mathrm{t}^{ - 1}}\mathrm{8 } + \mathrm{ co}{\mathrm{t}^{ - 1}}18 + {\cot ^{ - 1}}32 + .....

upto 100 terms, then

\alpha

View answer and explanation

Correct option: A

1.01

Option A (1.01) is correct because the sum of the series can be simplified using the arctangent subtraction formula, leading to

\alpha = 1.01

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