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Question

$\sin x\sin \frac{x}{2}\sin \frac{3x}{2}-\cos x\cos \frac{x}{2}\cos \frac{3x}{2}=-1/2$

score 2 · Answer 1

Đề bài như sau:$sin x.sin \frac{x}{2}.cos \frac{3x}{2}-cos x.cos \frac{x}{2}.cos \frac{3x}{2}=\frac{-1}{2}$

$\Leftrightarrow sin x(cos x-cos 2x)-cos x.(cos 2x+cos x)=-1$

$\Leftrightarrow sin x.cos x-sin xcos 2x-cos^2x-cos x.cos 2x=-1$

$\Leftrightarrow sin x.cos x+1-cos^2x-cos 2x(sin x+cos x)=0$

$\Leftrightarrow sin x(cos x+sin x)-cos 2x(sin x+cos x)=0$

$\Leftrightarrow (sin x-cos 2x)(sin x+cos x)=0$

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