Tính B = cos pi/11 + cos 3pi/11 + cos 5pi/11 + cos 7pi/11 + cos 9pi/11

* Hướng dẫn giải

Đáp án A

Với k = 1, 2, 3, 4, 5 ta có:

$$\begin{gathered} \cos \frac{\left(2k-1\right)\pi }{11}\sin \frac{\pi }{11}=\frac{1}{2}\left[\sin \frac{2k\pi }{11}-\sin \frac{\left(2k-2\right)\pi }{11}\right] \\ \Rightarrow B.\sin \frac{\pi }{11}=\frac{1}{2}\left[\left(\sin \frac{2\pi }{11}-\sin 0\right)+\left(\sin \frac{4\pi }{11}-\sin \frac{2\pi }{11}\right)+\mathrm{...}+\left(\sin \frac{10\pi }{11}-\sin \frac{8\pi }{11}\right)\right] \\ =\frac{1}{2}\sin \frac{10\pi }{11}=\frac{1}{2}\sin \frac{\pi }{11} \\ \Rightarrow B=\frac{1}{2} \end{gathered}$$