Simplify trigonometric expression using trigonometric identities I have the trigonometric expression: $$2\sin x +2\sin \left(\frac{\pi} {3} -x\right) $$
and it should simplified in: $$\sin x + \sqrt 3 \cos x$$ but I do not know what formulas to apply. Could you tell me how to simplify it?

Using the formula for $\sin (\alpha - \beta)$ you obtain
\begin{align}
  2&\sin x +2\sin \left(\frac{\pi} {3} -x\right)\\
= 2&\sin x +2\left[\sin \left(\frac{\pi} {3}\right) \cos x - \cos\left(\frac{\pi} {3}\right) \sin x\right]\\
= 2&\sin x + 2\left[{\sqrt 3 \over 2} \cos x - \frac 1 2 \sin x\right]\\[1ex]
= 2&\sin x + \sqrt 3  \cos x - \sin x\\[1em] =\ \, &\color{red}{\sin x + \sqrt 3  \cos x}
\end{align}
