prove that $\sqrt{2} \sin10^\circ+ \sqrt{3} \cos35^\circ= \sin55^\circ+ 2\cos65^\circ$ Question:
Prove that: $\sqrt{2} \sin10^\circ + \sqrt{3} \cos35^\circ = \sin55^\circ + 2\cos65^\circ$
My Efforts:
$$2[\frac{1}{\sqrt{2}}\sin10] + 2[\frac{\sqrt{3}}{2}\cos35]$$
$$= 2[\cos45 \sin10] + 2[\sin60 \cos35]$$

Hints:
$$\begin{align}&\bullet\;\;\sin(x+y)=\sin x\cos y+\sin y\cos x\\{}\\&\bullet\;\;\sin 45^\circ=\frac1{\sqrt2}=\frac{\sqrt2}2=\cos45^\circ\\{}\\&\bullet\;\;\cos x=\cos(-x)\end{align}$$
