# trig

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

csc θ = 1 + cot θ

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1. 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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posted by Reiny

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