(sin10°+sin20°)/(cos10°+cos20°)化简求值

(sin10°+sin20°)/(cos10°+cos20°) （和差化积得到下式）
=2sin15°cos5°/(2cos15°cos5°)
=tan15°
=tan(45°-30°)
=(1- tan30°)/(1+ tan30°)
=(1- 根号3/3)/(1+ 根号3/3)
=(3-根号3)/(3+根号3)
=(3-根号3)²/[(3+根号3)(3-根号3)]
=(12-6根号3)/6
=2 - 根号3sin10°+sin20°)/(cos10°+cos20°)（和差化积得到下式）=2sin15°cos5°/(2cos15°cos5°)能把这部分说详细点么？谢了sin10°+sin20°=sin(15°-5°)+sin(15°+5°)=(sin15°cos5° -cos15°sin5°) + (sin15°cos5° +cos15°sin5°)=2sin15°cos5°而：cos10°+cos20°=cos(15°-5°)+cos(15°+5°)=(cos15°cos5° +sin15°sin5°) + (cos15°cos5° -sin15°sin5°)=2cos15°cos5°所以：(sin10°+sin20°)/(cos10°+cos20°) =2sin15°cos5°/(2cos15°cos5°)