Với mọi góc ∝ , biểu thức cos ∝ + cos( ∝+ π/5 ) +cos( ∝ +2 π/5 ) +...+cos( ∝+9 π/5 ) nhận giá trị bằng bao nhiêu ?

$ A = \cos \alpha  + \cos \left( {\alpha  + \dfrac{\pi }{5}} \right) + \cos \left( {a + \dfrac{{2\pi }}{5}} \right) + ... + \cos \left( {\alpha  + \dfrac{{9\pi }}{5}} \right)\\ A = \left( {\cos \left( {a + \dfrac{\pi }{5}} \right) + \cos \left( {\alpha  + \dfrac{{6\pi }}{5}} \right)} \right) + \left( {\cos \left( {\alpha  + \dfrac{{2\pi }}{5}} \right) + \cos \left( {\alpha  + \dfrac{{7\pi }}{5}} \right)} \right) + .... + \left( {\cos \left( {\alpha  + \dfrac{{4\pi }}{5}} \right) + \cos \left( {\alpha  + \dfrac{{9\pi }}{5}} \right)} \right) + \cos \left( {\alpha  + \dfrac{{5\pi }}{5}} \right)\\ A = \cos \alpha  + \left( {\cos \left( {a + \dfrac{\pi }{5}} \right) - \cos \left( {\alpha  + \dfrac{\pi }{5}} \right)} \right) + \left( {\cos \left( {\alpha  + \dfrac{{2\pi }}{5}} \right) - \cos \left( {\alpha  + \dfrac{{2\pi }}{5}} \right)} \right) + ... + \left( {\cos \left( {\alpha  + \dfrac{{4\pi }}{5}} \right) - \cos \left( {\alpha  + \dfrac{{4\pi }}{5}} \right)} \right) - \cos \alpha \\ A = 0 $