Question

sin(4arccos(-1/2)-2arctg(sqrt3/3)

Answer 1

$sin(4arccos(-frac{1}{2})-2arstgfrac{sqrt{3}}{3})=sin(4*frac{2pi}{3}-2*frac{pi}{6})=$

 

$=sin(frac{8pi}{3}-frac{pi}{3})=sinfrac{7pi}{3}=sin(2pi+frac{pi}{3})=sinfrac{pi}{3}=frac{sqrt{3}}{2}$