precal

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sin^2x/cosx=sec^2x-1

  • precal -

    sin^2x /cosx = 1/cos^2 x - 1
    multiply each side by cos^2 x
    sin^2 x cosx = 1 - cos^2x
    (1 - cos^2x)cosx = 1 - cos^2x
    cosx - cos^3x - 1 + cos^2x = 0
    cos^3x - cos^2x - cosx + 1 = 0
    cos^2x(cosx - 1) -(cosx - 1) = 0
    (cosx-1)(cos^2x-1) =0
    (cosx-1)(cosx-1)(cosx+1) = 0
    cosx = 1 or cosx = -1
    x = 0, 2π or x = π

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