SOLUTION: solve over the interval [0,2π) tan(x/2)=√(3)/3

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Question 635237: solve over the interval [0,2π)
tan(x/2)=√(3)/3
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
solve over the interval [0,2π)
tan(x/2)=√(3)/3
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Identity: tan 2s=(2 tan s)/(1-tan^2 s)
tan x=tan 2(x/2)
=(2 tan x/2)/(1-tan^2 x/2)
=(2√3/3)/(1-tan^2 √3/3)
=(2√3/3)/(1-3/9)
=(2√3/3)/(1-1/3)
=(2√3/3)/(2/3)
=(2√3/2)
=√3
tan x=√3
x=π/3 and 4π/3 in quadrants I and III where tan>0