For n ∈ N, if cot⁻¹3 + cot⁻¹4 + cot⁻¹5 + cot⁻¹n = 4, then n is equal to ____.

JEE Main 2024 Mathematics question

For n ∈ N, if cot⁻¹3 + cot⁻¹4 + cot⁻¹5 + cot⁻¹n = , then n is equal to .

Answer: 47

Using tan⁻¹: tan⁻¹(1/3) + tan⁻¹(1/4) = tan⁻¹(7/11); adding tan⁻¹(1/5) gives

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Question ID VK-011755