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a sin t + b cos t = c: solve for sin t or cos t, then evaluate

This type of question, asked 2 times: CDS 2 2025, CDS 2 2026. All 3 questions below, oldest first.

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  1. Question 1

    CDS 2 2025

    32
    If 8sin⁡θ−cos⁡θ=48\sin\theta - \cos\theta = 4, where 0<θ<π/20 < \theta < \pi/2, then what is cosec θ\mathrm{cosec}\,\theta equal to?

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  2. Question 2

    CDS 2 2026

    43
    If 8sin⁡θ−cos⁡θ=48\sin\theta - \cos\theta = 4, where π6<θ<π3\frac{\pi}{6} < \theta < \frac{\pi}{3}, then what is sin⁡θ\sin\theta equal to ?

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  3. Question 3

    CDS 2 2026

    40
    If 3cos⁡θ+4sin⁡θ=43\cos\theta + 4\sin\theta = 4, where 0≤θ<π20 \le \theta < \frac{\pi}{2}, then what is 4cos⁡θ+3sin⁡θ4\cos\theta + 3\sin\theta equal to ?

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