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Đề bài như sau:$sin x.sin \frac{x}{2}.cos \frac{3x}{2}-cos x.cos \frac{x}{2}.cos \frac{3x}{2}=\frac{-1}{2}$$\Leftrightarrow sin x(cos x-cos 2x)-cos x.(cos 2x+cos x)=-1$$\Leftrightarrow sin x.cos x-sin xcos 2x-cos^2x-cos x.cos 2x=-1$$\Leftrightarrow sin x.cos x+1-cos^2x-cos 2x(sin x+cos x)=0$$\Leftrightarrow sin x(cos x+sin x)-cos 2x(sin x+cos x)=0$$\Leftrightarrow (sin x-cos 2x)(sin x+cos x)=0

Đề bài như sau:$sin x.sin \frac{x}{2}.cos \frac{3x}{2}-cos x.cos \frac{x}{2}.cos \frac{3x}{2}=\frac{-1}{2}$$\Leftrightarrow sin x(cos x-cos 2x)-cos x.(cos 2x+cos x)=-1$$\Leftrightarrow sin x.cos x-sin xcos 2x-cos^2x-cos x.cos 2x=-1$$\Leftrightarrow sin x.cos x+1-cos^2x-cos 2x(sin x+cos x)=0$$\Leftrightarrow sin x(cos x+sin x)-cos 2x(sin x+cos x)=0$$\Leftrightarrow (sin x-cos 2x)(sin x+cos x)=0$