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Prove that sec^(2) (tan ^(-1) 3) + cose...

Prove that `sec^(2) (tan ^(-1) 3) + cosec^(2)(cot^(-1)2) = 15`

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To prove that \( \sec^2(\tan^{-1} 3) + \csc^2(\cot^{-1} 2) = 15 \), we will follow these steps: ### Step 1: Define the angles Let \( a = \tan^{-1}(3) \) and \( b = \cot^{-1}(2) \). ### Step 2: Express \( \sec^2(a) \) in terms of \( \tan(a) \) From the definition of the secant function, we know: \[ ...
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