Với mọi alpha, biểu thức: A = cos alpha + cos(alpha + pi/5) +...+cos(alpha + 9pi/5

* Hướng dẫn giải

Đáp án C

$$\begin{gathered} A=cos\alpha +cos(\alpha +\frac{\pi }{5})+\mathrm{...}+cos(\alpha +\frac{9\pi }{5}) \\ A=\left[cos\alpha +cos(\alpha +\frac{9\pi }{5})\right]+\mathrm{...}+\left[cos(\alpha +\frac{4\pi }{5})+cos(\alpha +\frac{5\pi }{5})\right] \\ A=2cos(\alpha +\frac{9\pi }{10})cos\frac{9\pi }{10}+2cos(\alpha +\frac{9\pi }{10})cos\frac{7\pi }{10}+\mathrm{...}+2cos(\alpha +\frac{9\pi }{10})cos\frac{\pi }{10} \\ A=2cos(\alpha +\frac{9\pi }{10})\left(cos\frac{9\pi }{10}+cos\frac{7\pi }{10}+cos\frac{5\pi }{10}+cos\frac{3\pi }{10}+cos\frac{\pi }{10}\right) \\ A=2cos(\alpha +\frac{9\pi }{10})\left(2cos\frac{\pi }{2}cos\frac{2\pi }{5}+2cos\frac{\pi }{2}cos\frac{\pi }{5}+cos\frac{\pi }{2}\right) \\ A=2cos(\alpha +\frac{9\pi }{10}).0=0 \end{gathered}$$