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tan x = (sin t + cos t)/(sin t - cos t): find root 2 sin x

The same question, asked 2 times: CDS 2 2023*, CDS 1 2025. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2023

    28
    If tan⁡x=sin⁡θ+cos⁡θsin⁡θ−cos⁡θ\tan x = \dfrac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta}, π4<θ<π2\dfrac{\pi}{4} < \theta < \dfrac{\pi}{2}, then what is 2 sin⁡x\sqrt{2}\,\sin x equal to ?

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  2. Question 2

    CDS 1 2025

    33
    If tan⁡θ=sin⁡α−cos⁡αsin⁡α+cos⁡α\tan\theta = \frac{\sin\alpha - \cos\alpha}{\sin\alpha + \cos\alpha}, where θ\theta and α\alpha (α≠π4)\left(\alpha \ne \frac{\pi}{4}\right) are acute angles, then what is 2sin⁡θ\sqrt{2}\sin\theta equal to ?

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