$\begin{array}{l} A = \cos {20^o} + \cos {40^o} + \cos {60^o} + \cos {80^o}=A = \dfrac{1}{{\sin {{20}^o}}}\left( {\sin {{20}^o}\cos {{20}^o} + \sin {{20}^o}\cos {{40}^o} + \cos {{60}^o}\sin {{20}^o} + \cos {{80}^o}\sin {{20}^o}} \right)\\ A = \dfrac{1}{{2\sin {{20}^o}}}\left( {\sin {{40}^o} + \sin {{60}^o} - \sin {{20}^o} + \sin {{80}^o} - \sin {{40}^o} + \sin {{100}^o} - \sin {{60}^o}} \right)\\ A = \dfrac{1}{{2\sin {{20}^o}}}\left( {\sin {{100}^o} + \sin {{80}^o} - \sin {{20}^o}} \right)\\ A = \dfrac{1}{{2\sin {{20}^o}}}\left( {2\sin {{90}^o}\cos {{10}^o} - \sin {{20}^o}} \right)\\ A = \dfrac{1}{{2\sin {{20}^o}}}\left( {2\cos {{10}^o} - \sin {{20}^o}} \right)\\ A = \dfrac{1}{{2\sin {{20}^o}}}\left( {2\cos {{10}^o} - 2\sin {{10}^o}\cos {{10}^o}} \right)\\ A = \dfrac{{2\cos {{10}^o}\left( {1 - \sin {{10}^o}} \right)}}{{2\sin {{20}^o}}} = \dfrac{{2\cos {{10}^o}\left( {1 - \sin {{10}^o}} \right)}}{{4\sin {{10}^o}\cos {{10}^o}}} = \dfrac{{1 - \sin {{10}^o}}}{{2\sin {{10}^o}}} \end{array}$
Đến đoạn này thì không rút gọn được nữa.
