Bài 65 trang 219 SGK Đại số 10 Nâng cao

Đề bài

\({{\cos {{80}^0} - \cos {{20}^0}} \over {\sin {{40}^0}\cos {{10}^0} + \sin {{10}^0}\cos {{40}^0}}}\) bằng:

\(\eqalign{
& (A)\,\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(B)\,{{\sqrt 3 } \over 2} \cr
& (C)\,\, - 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(D)\, - {{\sqrt 3 } \over 2} \cr} \)

Hướng dẫn giải

Ta có:

\({{\cos {{80}^0} - \cos {{20}^0}} \over {\sin {{40}^0}\cos {{10}^0} + \sin {{10}^0}\cos {{40}^0}}} = {{ - 2\sin {{50}^0}\sin {{30}^0}} \over {\sin ({{40}^0} + {{10}^0})}} \)

\(=  - 2\sin {30^0} =  - 1\) 

Vậy chọn C