Question

已知點A（cos10°，sin10°）、B（sin40°，cos40°），則直線AB的傾斜角等于（　　）

A．135°

B．120°

C．105°

D．95°

Answer 1

設直線AB的傾斜角為α，則tanα=

cos40°-sin10°

sin40°-cos10°

=

cos(30°+10°)-sin10°

sin(30°+10°)-cos10°

=

cos30°cos10°-sin30°sin10°-sin10°

sin30°cos10°+cos30°sin10°-cos10°

=

3 2 cos10°- 3 2 sin10°

3 2 sin10°- 1 2 cos10°

=

3 (cos60°cos10°-sin60°sin10°)

cos30°sin10°-sin30°cos10°

=

3 cos70°

sin(-20°)

=-

3

．
因為0°≤α＜180°，所以α=120°．
故選B．