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If sin x + sin^2 x = 1 (or the cos form), find a power expression in the other ratio

The same question, asked 2 times: CDS 2 2018*, CDS 1 2019. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2018

    68
    If sin⁡2x+sin⁡x=1\sin^2 x + \sin x = 1, then what is the value of cos⁡12x+3cos⁡10x+3cos⁡8x+cos⁡6x\cos^{12} x + 3 \cos^{10} x + 3 \cos^8 x + \cos^6 x ?

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  2. Question 2

    CDS 1 2019

    32
    If cos⁡2x+cos⁡x=1\cos^2 x + \cos x = 1, then what is the value of sin⁡12x+3sin⁡10x+3sin⁡8x+sin⁡6x\sin^{12} x + 3\sin^{10} x + 3\sin^{8} x + \sin^{6} x ?

    Tap an option to check your answer.