Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Quiz for Lessons 14.6-14.7 - Page 962: 1

$\frac{\sqrt{3}-1}{2\sqrt2}$

Using the given identities and the known values: $\sin (\pi/12)=\sin(\pi/4)\cos(\pi/6)-\sin(\pi/6)\cos(\pi/4)=\frac{1}{\sqrt2}\frac{\sqrt3}{2}-\frac{1}{2}\frac{1}{\sqrt2}=\frac{\sqrt{3}-1}{2\sqrt2}$