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Solve the equation for x in the interval 0<x<2pi

1/ 1+tan^2x = -cos x

How would i do this? im thinking of maybe changing the 1+tan to sec^2x?

  • Math -

    Good idea. Use 1+tan^2 x = sec^2x
    1/(1+tan^2x) = -cos x
    1/sec^2x = -cosx
    cos^2x + cosx = 0
    cosx (cosx + 1) = 0
    cos x = 0 or -1
    x = pi/2, 3 pi/2 or pi

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