回复 1# 力工
硬来就行啦
\[\sin(4x)=2\sqrt{2}\sin(x)\sin(3x)\]
\[2\cos(x)\cos(2x)=\sqrt{2}\sin(3x)\]
\[\sqrt{2}\cos(x)\cos(2x)=\sin(x)\cos(2x)+\sin(2x)\cos(x)\]
\[\tan(x)+\tan(2x)=\sqrt{2}\]
\[\tan(x)+\frac{2\tan(x)}{1-\tan(x)^2}=\sqrt{2}\]
\[\tan(x)=\sqrt{2}\pm1\]
\[x=\arctan(\sqrt{2}\pm1)=\frac{\pi}{8} 或 \frac{3\pi}{8}\] |