Question

(sin10°+sin20°)/(cos10°+cos20°)化简求值

Answer 1

(sin10°+sin20°)/(co
s10
°+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3

Answer 2

解：原式=sin20°cos10°-cos(180°-20°)sin10°
=sin20°cos10°-(-cos20°)sin10°
(应用诱导公式)
=sin20°cos10°+cos20°sin10°
=sin(20°+10°)
(应用正弦和角公式)
=sin30°
=1/2。