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Prove that sin cot^(-1) tan cos^(-1) x =...

Prove that `sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x = x, " where " x in [0,1]`

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To prove that \( \sin(\cot^{-1}(\tan(\cos^{-1}(x)))) = \sin(\csc^{-1}(\cot(\tan^{-1}(x)))) = x \) for \( x \in [0, 1] \), we will break down the problem into two parts. ### Part 1: Proving \( \sin(\cot^{-1}(\tan(\cos^{-1}(x)))) = x \) 1. **Start with the inner function**: \[ \cos^{-1}(x) \] ...
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