Biểu thức \(1+\cos x+\cos2x\) có thể được biến đổi thành
\(4\cos x.\cos\left(\dfrac{x}{2}+\dfrac{\pi}{3}\right).\cos\left(\dfrac{x}{2}-\dfrac{\pi}{3}\right)\).\(4\cos x.\cos\left(\dfrac{x}{2}+\dfrac{\pi}{6}\right).\cos\left(\dfrac{x}{2}-\dfrac{\pi}{6}\right)\).\(4\cos x.\cos\left(\dfrac{x}{2}+\dfrac{\pi}{3}\right).\sin\left(\dfrac{x}{2}-\dfrac{\pi}{6}\right)\).\(4\cos x.\sin\left(\dfrac{x}{2}+\dfrac{\pi}{3}\right).\cos\left(\dfrac{x}{2}-\dfrac{\pi}{6}\right)\).Hướng dẫn giải:\(1+\cos x+\cos2x=\left(1+\cos2x\right)+\cos x=2\cos^2x+\cos x\)
\(=2\cos x\left[\cos x+\dfrac{1}{2}\right]=2\cos x\left(\cos x+\cos\dfrac{\pi}{3}\right)\)
\(=4\cos x.\cos\left(\dfrac{x}{2}+\dfrac{\pi}{6}\right).\cos\left(\dfrac{x}{2}-\dfrac{\pi}{6}\right)\)
