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The value of $\cot ({cosec}^{- 1} \frac{5}{3} + \tan^{- 1} \frac{2}{3})$ is

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Correct option is A

Let E=cot⁡cosec−1⁡53+tan−1⁡23⇒E=cot⁡tan−1⁡34+tan−1⁡23⇒E=cot⁡tan−1⁡34+231−34⋅23⇒E=cot⁡tan−1⁡176=617

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The value of cot⁡cosec−1⁡53+tan−1⁡23 is

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The value of $\cot ({cosec}^{- 1} \frac{5}{3} + \tan^{- 1} \frac{2}{3})$ is