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Solve <span title="(sin^2x)(cos3x)+(cos3x)(cos^2x)=(1/2)">(sin^2x)(cos3x)+(cos3x)(c...</span> for x over [0,2pi)?

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Solve (sin^2x)(cos3x)+(cos3x)(c... for x over [0,2pi)?

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  1. (sin^2x) (cos3x) + (cos3x)(cos^2x) =(1/2)

    take out common factor .. . .

    (cos 3x) [sin^2(x) + cos^2(x)] = 1/2 .. . .. . second factor = 1

    thus

    cos 3x = 1/2

    3x = π/3 , 5π/3 , 7π/3 , 11π/3 , 13π/3 , 17π/3

    thus

    x = π/9 , 5π/9 , 7π/9 , 11π/9 , 13π/9 , 17π/9

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