(2sin80-sin20)/2sin70
=[2sin(60+20)-sin20]/2sin70
=[2(sin60cos20+cos60sin20)-sin20]/2cos20
=(2sin60cos20+2cos60sin20-sin20)/2cos20
=(2sin60cos20+2×1/2sin20-sin20)/2cos20
=(2sin60cos20+sin20-sin20)/cos20
=(2sin60cos20)/2cos20
=sin60
=√3/2
(2sin80-sin20)/2sin70
=[2sin(60+20)-sin20]/2sin70
=[2(sin60cos20+cos60sin20)-sin20]/2cos20
=(2sin60cos20+2cos60sin20-sin20)/2cos20
=(2sin60cos20+2×1/2sin20-sin20)/2cos20
=(2sin60cos20+sin20-sin20)/cos20
=(2sin60cos20)/2cos20
=sin60
=√3/2