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trig

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Can someone please help me solve this equation?

Solve the equation in the interval [0°, 360°).

csc θ = 1 + cot θ

  • trig -

    1/sinθ = 1 + cosθ/sinθ
    1 = sinθ + cosθ
    1 - sinθ = cosθ
    1-2sinθ + sin^2 θ = cos^2 θ
    1 - 2sinθ + sin^2 θ = 1 - sin^2 θ
    2sin^2 θ - 2sinθ = 0
    2sinθ(sinθ - 1) = 0
    sinθ = 0, θ = 0,180,360°
    or sinθ = 1 , θ = 90°

    but,...
    since we squared, all our answers must be verified.
    since csc x is undefined for x = 0,180, 360 none of those will work

    so x = 90°

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