sin20sin40sin60sin80=√3/2*sin20sin40sin80=√3/2*½(cos20-cos60)*sin80=√3/4*(cos20-½)*sin80=√3/8*(2cos20-1)*sin80=√3/8(2cos20sin80-sin80)==√3/8*(2*½(sin60+sin100)-sin80)=√3/8*(sin60+sin100-sin80)=√3/8*(√3/2+sin100-sin80)=√3/8*(√3/2+cos(90+10)-sin(90-10))=√3/8*(√3/2+cos10-cos10)==√3/8*(√3/2+0)=√3/8*√3/2=3/16