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cos^2x-sinxcosx-1/2=o

  • math -

    dropping the x's for brevity,

    2cos^2 - 1 = 2sin cos
    4cos^4 - 4cos^2 + 1 = 4sin^2 cos^2
    4cos^4 - 4cos^2 + 1 = 4(1-cos^2) cos^2
    4cos^4 - 4cos^2 + 1 = 4cos^2 - 4cos^4
    8cos^4 - 8cos^2 + 1 = 0
    cos^2 = 1/4 (2 ± √2)
    x = kπ/2 ± π/8 for integer k

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