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$\cos 3x+\cos x=2\cos x(\sin 2x+1)$$\Leftrightarrow 2\cos 2x\cos x=2\cos x(\sin 2x+1)$$\Leftrightarrow 2\cos x(\cos 2x-\sin 2x-1)=0$$\Leftrightarrow \cos x=0$ hoặc $\cos 2x-\sin 2x-1=0$(1)Từ (1) $\Rightarrow \cos x^{2}-\sin x^{2}=2\sin x\cos x+1$$\Leftrightarrow -2\sin x(\sin x-\cos x)=0 $ $\Rightarrow \sin x=0 $ hoặc $ \sin x-\cos x=0$$\Rightarrow 1-2\sin x\cos x=0$ $\Leftrightarrow \sin 2x=1$

$\cos 3x\cos x=2\cos x(\sin 2x+1)$$\Leftrightarrow 2\cos 2x\cos x=2\cos x(\sin 2x+1)$$\Leftrightarrow 2\cos x(\cos 2x-\sin 2x-1)=0$$\Leftrightarrow \cos x=0$ hoặc $\cos 2x-\sin 2x-1=0$(1)Từ (1) $\Rightarrow \cos x^{2}-\sin x^{2}=2\sin x\cos x+1$$\Leftrightarrow -2\sin x(\sin x-\cos x)=0 $ $\Rightarrow \sin x=0 $ hoặc $ \sin x-\cos x=0$$\Rightarrow 1-2\sin x\cos x=0$ $\Leftrightarrow \sin 2x=1$

$\cos 3x\cos x=2\cos x(\sin 2x+1)$$\Leftrightarrow 2\cos 2x\cos x=2\cos x(\sin 2x+1)$$\Leftrightarrow 2\cos x(\cos 2x-\sin 2x-1)=0$$\Leftrightarrow \cos x=0$ hoặc $\cos 2x-\sin 2x-1=0$(1)$\Rightarrow x=pi/2+kpi$ Từ (1) $\Rightarrow \cos x^{2}-\sin x^{2}=2\sin x\cos x+1$$\Leftrightarrow -2\sin x(\sin x-\cos x)=0 $ $\Rightarrow \sin x=0 $ hoặc $ \sin x-\cos x=0$$\Rightarrow 1-2\sin x\cos x=0$ $\Leftrightarrow \sin 2x=1$ $\Rightarrow 2x=pi/2+k2pi$ $\Rightarrow x= pi/4+kpi$