Tính E = sin pi/5 + sin 2pi/5 +...+ sin 9pi/5. 0

* Hướng dẫn giải

Đáp án A

$$\begin{gathered} E=\sin \frac{\pi }{5}+\sin \frac{2\pi }{5}+\mathrm{...}+\sin \frac{9\pi }{5} \\ =\left(\sin \frac{\pi }{5}+\sin \frac{9\pi }{5}\right)+\left(\sin \frac{2\pi }{5}+\sin \frac{8\pi }{5}\right)+\mathrm{...}+\left(\sin \frac{4\pi }{5}+\sin \frac{6\pi }{5}\right)+\sin \frac{5\pi }{5} \\ =\left[\sin \frac{\pi }{5}+\sin \left(2\pi -\frac{\pi }{5}\right)\right]+\left[\sin \frac{2\pi }{5}+\sin \left(2\pi -\frac{2\pi }{5}\right)\right]+\mathrm{...}+\left[\sin \frac{4\pi }{5}+\sin \left(2\pi -\frac{4\pi }{5}\right)\right]+\sin \pi \\ =\left[\sin \frac{\pi }{5}+\sin \left(-\frac{\pi }{5}\right)\right]+\left[\sin \frac{2\pi }{5}+\sin \left(-\frac{2\pi }{5}\right)\right]+\mathrm{...}+\left[\sin \frac{4\pi }{5}+\sin \left(-\frac{4\pi }{5}\right)\right]+0 \\ =\left(\sin \frac{\pi }{5}-\sin \frac{\pi }{5}\right)+\left(\sin \frac{2\pi }{5}-\sin \frac{2\pi }{5}\right)+\mathrm{...}+\left(\sin \frac{4\pi }{5}-\sin \frac{4\pi }{5}\right) \\ = 0 + 0 + \dots + 0 = 0 \end{gathered}$$