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Prove that tan^(-1) x + cot^(-1) (x+1) ...

Prove that `tan^(-1) x + cot^(-1) (x+1) = tan ^(-1) (x^(2) + x+1)`.

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To prove that \( \tan^{-1} x + \cot^{-1} (x+1) = \tan^{-1} (x^2 + x + 1) \), we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS). ### Step 1: Write the LHS We start with the left-hand side: \[ LHS = \tan^{-1} x + \cot^{-1} (x + 1) \] ...
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