Question

Chứng minh rằng : \(\cos^2x+\cos^2\left(\frac{\pi}{3}+x\right)+\cos^2\left(\frac{2\pi}{3}+x\right)=\frac{3}{2}\)

Answer 1

Ta có \(A=\frac{3}{2}+\frac{1}{2}\left[\cos2x+\cos\left(\frac{2\pi}{3}+2x\right)+\cos\left(\frac{4\pi}{3}+2x\right)\right]\)

            \(=\frac{3}{2}+\frac{1}{2}\left[\cos2x+2\cos\left(\pi+2x\right).\cos\left(-\frac{\pi}{3}\right)\right]=\frac{3}{2}+\frac{1}{2}\left[\cos2x+\cos2x\right]=\frac{3}{2}\)