How is this" Sine function" solved?

Question

I got a question that says:

If the graph of $y=\sin3x$ is shifted $\frac{\pi}{18}$ units horizontally to the left, then the equation of the new graph is

A) $y=\frac{\sqrt3}{2}\sin3x+\frac{1}{2}\cos3x$

B) $y=\frac{1}{2}\sin3x-\frac{1}{2}\cos3x$

C) $y=-\frac{\sqrt3}{2}\sin3x+\frac{1}{2}\cos3x$

With the help of a calculator, I found out that the answer is A, but I don't know how to do it without a calculator. I tried many times, but I didn't succeed. I know that the way to solve this problem is related to what is called "Reduction Identity," but I don't get how to use it.

Answer 1

$$y = \sin\left(3\left(x + \frac{\pi}{18}\right)\right) = \dots\qquad(\textrm{expand it})$$

Answer 2

HINT Use the answer provided by uraf and use the property: $$\sin(a+b)=\sin b\cos a+\sin a\cos b$$