Question

csc 2pi/3

Answer 1

\(\large\color{blue}{ \rm csc(2π/3)=csc(\frac{2(180)}{3})=csc(120)}\)

\(\large\color{blue}{ \rm csc(120)=1~/~sin(120)}\)

\(\large\color{blue}{ \rm sin(120)=sin(60+60)=sin(60)cos(60)+sin(60)cos(60)}\)
\(\large\color{blue}{ \rm 2sin(60)cos(60)=2(√3~/~2)(1/2)=√3~/~2}\)

hence csc 120 = 2/√3 = 2√3 / 3