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sin x + sin^2 x = 1 (or a similar form): evaluate a power expression

This type of question, asked 5 times: CDS 2 2016, CDS 1 2018, CDS 2 2018, CDS 1 2019, CDS 2 2026. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    72
    If sin⁡x+sin⁡2x=1\sin x + \sin^2 x = 1, then what is the value of cos⁡8x+2cos⁡6x+cos⁡4x\cos^8 x + 2\cos^6 x + \cos^4 x ?

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  2. Question 2

    CDS 1 2018

    61
    If cos⁡x+cos⁡2x=1\cos x + \cos^2 x = 1, then what is sin⁡2x+sin⁡4x\sin^2 x + \sin^4 x equal to ?

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  3. Question 3

    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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  4. Question 4

    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 ?

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  5. Question 5

    CDS 2 2026

    38
    If cos⁡2x+cos⁡4x=1\cos^2 x + \cos^4 x = 1, where 0<x<π20 < x < \frac{\pi}{2}, then what is (sin⁡2x+sin⁡3x)+(sin⁡3x+sin⁡4x)(\sin^2 x + \sin^3 x) + (\sin^3 x + \sin^4 x) equal to ?

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