1+cos20°2sin20°-sin10°（1tan5°-tan5°）=（）A.32B.22C.1D.2

Question

(1+cos20°)/(2sin20°)-sin10°（(1)/(tan5°)-tan5°）=（　　）

A.

(√(3))/(2)

B.

(√(2))/(2)

C. 1

D. 2

Answer 1

(1+cos20°)/(2sin20°)-sin10°（(1)/(tan5°)-tan5°）
=(2cos210°)/(4sin10°cos10°)-sin10°((cos5°)/(sin5°)-(sin5°)/(cos5°))
=(cos10°)/(2sin10°)-2sin5°cos5°•(cos25°-sin25°)/(sin5°cos5°)
=(cos10°)/(2sin10°)-2cos10°
=(cos10°-4sin10°cos10°)/(2sin10°)
=(cos10°-2sin20°)/(2sin10°)
=(cos10°-2sin(30°-10°))/(2sin10°)
=(cos10°-2(sin30°cos10°-cos30°sin10°))/(2sin10°)
=cos30°
=(√(3))/(2)．
故选：A．