<s>[INST] Simplify $5(3 \sin(x) + \sqrt3 \cos(x))$ So Wolfram tells me I can reach $10 \sqrt3 \sin(x + π/6)$ from this expression, but I cant grasp how to do it. Any help is appreciated.
 [/INST] Given these identities:
$$\frac{1}{2}\sqrt{3} = \cos(\frac{\pi}{6})$$
$$\frac{1}{2} = \sin(\frac{\pi}{6})$$
$$\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \sin(\beta)\cos(\alpha)$$
We get:
$$5(3\sin(x) + \sqrt{3}\cos(x)) = $$
$$5\sqrt{3}(\sqrt{3}\sin(x) + \cos(x)) =$$
$$10\sqrt{3}(\cos(\frac{\pi}{6})\sin(x) + \frac{1}{2}\cos(x)) =$$
$$10\sqrt{3}(\cos(\frac{\pi}{6})\sin(x) + \sin(\frac{\pi}{6})\cos(x)) =$$
$$10\sqrt{3}\sin(x + \frac{\pi}{6})$$
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