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Find all solutions in the interval [0, pi], 2sec^2x+tan^2x-3=0

  • pre cal 2 - ,

    2sec^2x+tan^2x-3=0
    2/cos^2x + sin^2x/cos^2x - 3 = 0
    multiply by cos^2x
    2 + sin^2x - 3cos^2x = 0
    2 + (1 - cos^2x) - 3cos^2x = 0
    3 = 4 cos^2x
    cos^2 = 3/4
    cosx = ± √3/2
    x = 30° , 150° , 210° , or 330°
    x = π/6, 5π/6 , 7π/6, or 11π/6

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