**Proof.**Recall that we have the next addition formula for Sine:

\begin{align*} \sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B). \end{align*}

\begin{align*} \sin(x + x) = \sin(x)\cos(x) + \cos(x)\sin(x) &\iff \sin(2x) = 2\sin(x)\cos(x), \end{align*}

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## Prove that sin(2x) = 2sin(x)cos(x)

Show that \sin(2x) is equal to 2\sin(x)\cos(x).

**Proof.** Recall that we have the next addition formula for Sine:
Now take A = B = x. Then we get:
which is the desired result. Therefore, \sin(2x) is equal to 2\sin(x)\cos(x).

\begin{align*} \sin(A+B) = \sin(A)\cos(B) + \cos(A)\sin(B). \end{align*}