JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
For \(n \in N\), if \(\cot ^{-1} 3+\cot ^{-1} 4+\cot ^{-1} 5+\cot ^1 n=\frac{\pi}{4}\), then \(\mathrm{n}\) is equal to .........
- A \(70\)
- B \(56\)
- C \(10\)
- D \(47\)
Answer & Solution
Correct Answer
(D) \(47\)
Step-by-step Solution
Detailed explanation
\( \cot ^{-1} 3+\cot ^{-1} 4+\cot ^{-1} 5+\cot ^1 n=\frac{\pi}{4} \) \( \tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{4}+\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{n}=\frac{\pi}{4} \) \( \tan ^{-1}\left(\frac{46}{48}\right)+\tan ^{-1} \frac{1}{n}=\frac{\pi}{4} \)…
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