Expand the Trigonometric Expression sin(pi/6-x)

$\sin (\frac{π}{6} - x)$

Apply the difference of angles identity.

$\sin (\frac{π}{6}) \cos (x) - \cos (\frac{π}{6}) \sin (x)$

Simplify each term.

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{1}{2} \cos (x) - \cos (\frac{π}{6}) \sin (x)$

Combine $\frac{1}{2}$ and $\cos (x)$ .

$\frac{\cos (x)}{2} - \cos (\frac{π}{6}) \sin (x)$

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\cos (x)}{2} - \frac{\sqrt{3}}{2} \sin (x)$

Combine $\sin (x)$ and $\frac{\sqrt{3}}{2}$ .

$\frac{\cos (x)}{2} - \frac{\sin (x) \sqrt{3}}{2}$