Question

一道高一数学题目~~！

（1）COT 10度+TAN 15度=？
A.1/SIN 5度 B.1/COS 5度 C.1/SIN 10度 D.1/COS 10度
（2）COS 36度-COS 72度=？
（3）COS 24度+COS 48度-COS 12度-COS 84度=？
写过程，谢谢~~！

Answer 1

2sin36(COS36-COS72)
=sin72-2sin36cos72
=sin72-(sin108+sin(-36))=sin36
故cos36-cos72=1/2

(3)cos24+cos48-cos12-cos84
=(cos24-cos84)+(cos48-cos12)
=-2sin54sin(-30)-2sin30sin18(和差化积)
=sin54-sin18
=cos36-cos72
=1/2 (见上题)

Answer 2

因为度数不好打,所以,所有数字都省略了度数的符号
(1)cot10+tan15
=cos10/sin10+sin15/cos15
=(cos10cos15+sin15sin10)/(sin10cos15)
=cos(10-15)/(sin10cos15)
=cos5/(2sin5cos5cos15)
=1/(2sin5cos15)
=1/[2sin5(cos10cos5-sin10sin5)]
=1/(cos10sin10-sin10cos10+sin10)
=1/sin10
故选C