SOLUTION: how do i solve tan 2pi/3 using the half angle identity?

Question 693702: how do i solve tan 2pi/3 using the half angle identity?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
how do i solve tan 2pi/3 using the half angle identity?
Identity: tanx/2=sin x/(1-cos x)
tan(2π/3)=tan(4π/3)/2=sin(4π/3)/(1-cos(4π/3))
sin(4π/3)=-√3/2 (in quadrant III where sin<0)
cos(4π/3)=-1/2 (in quadrant III where cos<0)
tan(2π/3)=-√3/2/(1+1/2)=-(√3/2)/(3/2)=-√3/3
..
check with calculator:
tan(2π/3)=-0.5773..(in quadrant II where tan <0)
-√3/3=-.5773..
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