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sec^2(tan^-1 a), tan^2(sec^-1 b) and similar, using 1 + tan^2 = sec^2

This type of question, asked 3 times: 11 May 2024 S1, 23 Apr 2025 S1, 18 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    11 May 2024 S1

    118
    The value of sec⁡2(tan⁡−12)+csc⁡2(cot⁡−13)\sec^2(\tan^{-1} 2) + \csc^2(\cot^{-1} 3) is

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  2. Question 2

    23 Apr 2025 S1

    129
    The value of tan⁡2(sec⁡−14)+cot⁡2(csc⁡−13)\tan^{2}\left( \sec^{- 1}4 \right)+\cot^{2}\left( \csc^{- 1}3 \right) is

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  3. Question 3

    18 Apr 2026 S2

    68
    sec⁡2(tan⁡−13)−tan⁡2(sec⁡−13)=\sec^2(\tan^{-1}3) - \tan^2(\sec^{-1}3) =

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