Trigonometry

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Find all the angles between 0° and 90° which satisfy the equation
sec²Θcosec²Θ + 2cosec²Θ = 8

  • Trigonometry -

    multiply by sin^2 cos^2 to get

    1 + 2 cos^2 = 8 sin^2 cos^2
    8cos^4 - 6cos^2 + 1 = 0
    (4cos^2 - 1)(2 cos^2 - 1)

    so,

    cos^2 = 1/4 or 1/2
    cos = 1/2 or -1/2 or 1/√2 or -1/√2
    skip the negative values, since we want 1st quadrant angles only

    Θ = 45° or 60°

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