Express $$\dfrac{\sqrt{3} }{2}\sin x+\dfrac{1}{2}\cos x $$ in terms of sum of angles for sines function.

Question

Express $$\dfrac{\sqrt{3} }{2}\sin x+\dfrac{1}{2}\cos x $$     in terms of sum of angles for sines function.

Uniteasy Admin · Accepted Answer

$$\dfrac{\sqrt{3} }{2}\sin x+\dfrac{1}{2}\cos x $$
$$= \cos \dfrac{\pi}{6} \sin x+ \sin \dfrac{\pi}{6}\cos x$$
$$=\sin (x+\dfrac{\pi}{6}) $$