Question 693702
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(4&#960;/3)=-&#8730;3/2 (in quadrant III where sin<0)
cos(4&#960;/3)=-1/2 (in quadrant III where cos<0)
tan(2&#960;/3)=-&#8730;3/2/(1+1/2)=-(&#8730;3/2)/(3/2)=-&#8730;3/3
..
check with calculator:
tan(2&#960;/3)=-0.5773..(in quadrant II where tan <0)
-&#8730;3/3=-.5773..