Tính C = cos 2pi/11 + cos 4pi/11 + cos 6pi/11 + cos 8pi/11 + cos 10pi/11

* Hướng dẫn giải

Đáp án D

Với k = 1, 2, 3, 4, 5 ta có:

$$\begin{gathered} \cos \frac{\left(2k\right)\pi }{11}\sin \frac{\pi }{11}=\frac{1}{2}\left[\sin \frac{(2k+1)\pi }{11}-\sin \frac{\left(2k-1\right)\pi }{11}\right] \\ \Rightarrow C.\sin \frac{\pi }{11}=\frac{1}{2}\left[\left(\sin \frac{3\pi }{11}-\sin \frac{\pi }{11}\right)+\left(\sin \frac{5\pi }{11}-\sin \frac{3\pi }{11}\right)+\mathrm{...}+\left(\sin \frac{11\pi }{11}-\sin \frac{9\pi }{11}\right)\right] \\ =-\frac{1}{2}\sin \frac{\pi }{11} \\ \Rightarrow C=-\frac{1}{2} \end{gathered}$$