Question 1003087: Use trigonometric identities to solve tan(2θ)+tan(θ)=0 exactly for 0≤θ≤π.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Use trigonometric identities to solve tan(2x)+tan(x)=0 exactly
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tan(2x) = 2tan(x)/(1 - tan^2(x))
--> 2tan(x)/(1 - tan^2(x)) + tan(x) = 0
tan(x) = 0
--> x = 0, pi
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2/(1 - tan^2(x)) + 1 = 0
2/(1 - tan^2(x)) = -1
(1 - tan^2(x))/2 = -1
1 - tan^2(x) = -2
tan^2(x) = 3
x = sqrt(3)
--> x = pi/3, 4pi/3
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x = -sqrt(3)
--> x = 2pi/3, 5pi/3
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That's theta from 0 to 2pi. If you only want up to pi eliminate the others.
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