What is sinxcosx?
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# What is $\mathrm{sin}\left(x\right)\mathrm{cos}\left(x\right)$?

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## Method $1$:We know that, $2\mathrm{sin}x\mathrm{cos}x=\mathrm{sin}2x$Divide both sides by $2$, we get $\mathrm{sin}x\mathrm{cos}x=\frac{1}{2}\left(\mathrm{sin}2x\right)$ Method $2$:We know that, $\mathrm{sin}\left(A+B\right)=\mathrm{sin}A\mathrm{cos}B+\mathrm{cos}A\mathrm{sin}B$substitute $A=B=x$, we get $\mathrm{sin}\left(x+x\right)=\mathrm{sin}x\mathrm{cos}x+\mathrm{cos}x\mathrm{sin}x$$⇒$ $\mathrm{sin}2x=2\mathrm{sin}x\mathrm{cos}x$$⇒$ $\frac{1}{2}\left(\mathrm{sin}2x\right)=\mathrm{sin}x\mathrm{cos}x$

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