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

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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This question has some explanations "from the first principles". –  Dan Shved Nov 8 '13 at 10:29

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

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This is just solving a mystery by appealing to a bigger mystery ) –  Dan Shved Nov 8 '13 at 10:23
Although who knows, maybe the problem was indeed in making this connection... –  Dan Shved Nov 8 '13 at 10:24
@Dan Shved: Yes, I hope that if OP don't know $\sin(x+y)$, he will ask this. –  Boris Novikov Nov 8 '13 at 10:27
This was actually a good answer, since I didn't thaugt about that formula. –  theva Nov 8 '13 at 11:02

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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