Why is $\sin(t)\cos(t)$ equal to $\frac{1}{2}\sin(2t)$?

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I know that $\sin(t)\cos(t)$ is equal to $\frac{1}{2}\sin(2t)$ but I do not understand why, please explain it to me!

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2 Answers

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$\sin 2t =\sin (t+t)= \sin t \cos t+ \cos t\sin t =\ldots$.

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We now that: $$\sin(2t)=\frac{1}{2}\sin t\cos t/:\frac{1}{2}$$ Now we have: $$\frac{1}{2}\sin(2t)=\sin t\cos t$$

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