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sin^4 + cos^4 given: find sin t cos t

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

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  1. Question 1

    CDS 1 2025

    21
    If 2sin⁡4α+2cos⁡4α−1=02 \sin^4 \alpha + 2 \cos^4 \alpha - 1 = 0, where 0≤α<π/20 \le \alpha < \pi/2, then what is sin⁡2α+cos⁡2α\sin 2\alpha + \cos 2\alpha equal to ?

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  2. Question 2

    CDS 2 2026

    39
    If sin⁡4x+cos⁡4x=1\sin^4 x + \cos^4 x = 1, where 0≤x≤π20 \le x \le \frac{\pi}{2}, then what is sin⁡x⋅cos⁡x\sin x \cdot \cos x equal to ?

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