Question

[Nguyệt Hà Đỗ]

Chứng minh \(\frac{\cos3\alpha+\cos\alpha}{\sin3\alpha+\sin\alpha}.\tan2\alpha-8\sin^2\alpha.\cos^2\alpha=\cos4\alpha\)  với  \(\alpha\ne k\frac{\pi}{4}\left(k\in Z\right)\)

Answer 1

[Nguyễn Thái Bình]

\(VT=\frac{2\cos2\alpha.\cos\alpha}{2.\sin2\alpha\cos\alpha}.\frac{\sin2\alpha}{\cos2\alpha}-2\left(2\sin\alpha.\cos\alpha\right)^2\)

\(VT=1-2\left(\sin2\alpha\right)^2=\cos4\alpha\)