我们一个个来算,
(1+cos20°)/(2sin20°)=2cos²10°/(4sin10°cos10°)=cos10°/(2sin10°),
而cot5°-tan5°
=cos5°/sin5°-sin5°/cos5°
=(cos²5°-sin²5°)/(sin5°cos5°)
=cos10°/(1/2sin10°)
=2cos10°/sin10°,
所以原式=cos10°/(2sin10°)-2cos10°
= (cos10°-2sin20°)/(2sin10°)
=[cos10°-2sin(30°-10°)]/(2sin10°)
=(2cos30°sin10°))/(2sin10°)
=cos30°
=√3/2.