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Evaluate:cot-1(cot \(\frac{4\pi}3\)) |
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Answer» cot \(\frac{4\pi}3\) can be written as cot\((\pi+\frac{\pi}3)\) We know cot(π + θ) = cot (θ) ∴ cot\((\pi+\frac{\pi}3)\) = cot \((\frac{\pi}3)\) Now the question becomes cot-1(cot \(\frac{\pi}3\)) cot-1(cot x) = x Provided x ∈ (0, π) ∴ cot–1(cot \(\frac{4\pi}3\)) = \(\frac{\pi}3.\) |
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