Tính giá trị của G = cos^2 pi/6 + cos^2 2pi/6 +...+ cos^2 5pi/6 + cos^2 pi

* Hướng dẫn giải

Đáp án A

$$\begin{gathered} G={\cos }^2\frac{\pi }{6}+{\cos }^2\frac{2\pi }{6}+\mathrm{...}+{\cos }^2\frac{5\pi }{6}+{\cos }^2\pi \\ =\left({\cos }^2\frac{\pi }{6}+{\cos }^2\frac{2\pi }{6}\right)+\left({\cos }^2\frac{4\pi }{6}+{\cos }^2\frac{5\pi }{6}\right)+\left({\cos }^2\frac{\pi }{2}+{\cos }^2\pi \right) \\ =\left({\cos }^2\frac{\pi }{6}+{\cos }^2\frac{\pi }{3}\right)+\left({\cos }^2\frac{2\pi }{6}+{\cos }^2\frac{\pi }{6}\right)+1 \\ =2\left({\cos }^2\frac{\pi }{6}+{\cos }^2\frac{2\pi }{6}\right)+1 \\ =2\left({\cos }^2\frac{\pi }{6}+{\cos }^2\frac{\pi }{6}\right)+1=3 \end{gathered}$$