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tan A = cot B (or tan A tan B = 1) gives A + B = 90 degrees: find the angle

This type of question, asked 5 times: CDS 1 2020, CDS 2 2023, CDS 1 2024, CDS 1 2025, CDS 2 2026. All 5 questions below, oldest first.

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  1. Question 1

    CDS 1 2020

    54
    If tan⁡6θ=cot⁡2θ\tan 6\theta = \cot 2\theta, where 0<6θ<π20 < 6\theta < \frac{\pi}{2}, then what is the value of sec⁡4θ\sec 4\theta?

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  2. Question 2

    CDS 2 2023

    27
    Which one of the following is a value of θ\theta, if θ\theta satisfies the equation tan⁡2θtan⁡4θ−1=0\tan 2\theta \tan 4\theta - 1 = 0; 0<θ<π20 < \theta < \dfrac{\pi}{2} ?

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  3. Question 3

    CDS 1 2024

    51
    If tan⁡(3A)=cot⁡(A−22∘)\tan(3A) = \cot(A - 22^\circ), where 3A is an acute angle, then what is the value of A ?

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  4. Question 4

    CDS 1 2025

    35
    What is the value of x, where 0≤x<30∘0 \le x < 30^\circ, satisfying tan⁡3xtan⁡6x=1\tan 3x \tan 6x = 1 ?

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  5. Question 5

    CDS 2 2026

    36
    If tan⁡6θ⋅tan⁡3θ=1\tan 6\theta \cdot \tan 3\theta = 1, where 0<θ<30∘0 < \theta < 30^\circ, then what is θ\theta equal to ?

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