AP EAMCET · Maths · Inverse Trigonometric Functions
\(\cot \left[\sum_{n=3}^{32} \cot ^{-1}\left(1+\sum_{k=1}^n 2 k\right)\right]=\)
- A \(\frac{10}{3}\)
- B \(\frac{8}{3}\)
- C \(\frac{14}{3}\)
- D \(\frac{16}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{10}{3}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \because \sum_{k=1}^n 2 k=n(n+1) \\ & \therefore \cot \left(\sum_{n=3}^{32} \cot ^{-1}\left(1+\sum_{k=1}^n 2 k\right)\right) \\ & =\cot \left(\sum_{n=3}^{32} \cot ^{-1}(1+n(n+1))\right) \\ & =\cot \left(\sum_{n=3}^{32} \tan ^{-1}\left(\frac{(n+1)-n}{1+(n+1)…
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