1/sin10°-根号3/sin80°
= (sin 80 °- 根号3sin 10°)/sin10°sin80°
=2(1/2cos10°-根号3/2sin10°)/1/2sin10°cos10°
=2(sin30°cos10-cos30°-sin10°)/1/2sin20°
=2sin20°/1/2sin20°
=4
1/sin10°-根号3/sin80°
= (sin 80 °- 根号3sin 10°)/sin10°sin80°
=2(1/2cos10°-根号3/2sin10°)/1/2sin10°cos10°
=2(sin30°cos10-cos30°-sin10°)/1/2sin20°
=2sin20°/1/2sin20°
=4