Вычислите: sin(2arcsin(-1/2)+п/3)

Question

Вычислите: sin(2arcsin(-1/2)+п/3)

Answer 1

Sin[2arcsin(-1/2)+π/3]=sin[2*(7π/6)+π/3]=sin[(7π/3)+π/3]=
=sin(8π/3) = sin((9π/3)+π/3) = sin(π-π/3)=sin(π/3)=√3/2