Answer:
The simplification is done below.
Step-by-step explanation:
[tex](\sin(\frac{\pi}{6})\cos(\frac{\pi}{4}) - \sin(\frac{\pi}{4})\cos(\frac{\pi}{6}))^{2}[/tex]
= [tex](\frac{1}{2} \times \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2})^{2}[/tex]
=[tex]((\frac{1}{2\sqrt{2}}) \times (1 - \sqrt{3}))^{2}[/tex]
= [tex]0.125 \times (1 - (2 \times \sqrt{3}) +3)[/tex]
