# How to convert $3\sin(x)\cos(x)$ into expression involving only $\sin (x)$

I need to convert $3\sin(x)\cos(x)$ to an expression involving only $\sin (x)$, but I don't know how.

Can you please point me to solutions.

Thanks!!!

EDIT:

I can do something like this: $$3\sin(x)\sin(\frac{\pi}{2}-x)$$ but how can I convert this so that I have only $\sin(x)$ ?

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$\sin(2x)=2\sin x\cos x$. –  David Mitra Feb 8 at 13:19
$\cos x=\sqrt {1-\sin^2 x}$ (care with signs required) –  Mark Bennet Feb 8 at 13:20
@DavidMitra Thanks for the answer, but can you explain to me what have you written –  depecheSoul Feb 8 at 13:26
OK, I got is $sin(2x)=sin(x+x)=...$. It is adding two –  depecheSoul Feb 8 at 13:27
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## 1 Answer

Use the double angle formula for $\sin(2x)$: $$2\sin x \cos x = \sin(2x)\;\text{ and }\;\sin x \cos x = \frac 12 \sin(2x)$$

$$3\sin x \cos x = 2\sin x \cos x + \sin x \cos x = \sin(2x) + \frac 12 \sin (2x) = \dfrac 32 \sin (2x)$$

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I did it a little diffrently $3*\sin(x)*\cos(x)=3*(\frac{2}{2})*\sin(x)*\cos(x)=(\frac{3}{2})*\sin(2x)$ –  depecheSoul Feb 8 at 13:51
That's just fine! ;-) –  amWhy Feb 8 at 13:58
Sorry to say that all the answers did not satisfy the requirement - "convert 3sin(x)cos(x) to an expression involving only sin(x)". [:-)] Maybe the owner of the problem needed to edit his/her statement to reflect the actual required. –  Mick Feb 8 at 14:57
Nice answer and deserves $\checkmark$. –  Sami Ben Romdhane Feb 8 at 17:06
Good basic points. Enough for killing the problem. Hi :-) –  B. S. Feb 8 at 18:09
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