ANSWER
[tex]-\frac{\sqrt[]{3}}{2}[/tex]EXPLANATION
Given
[tex]\begin{gathered} \cos \text{ 150} \\ \end{gathered}[/tex]We can find cos 150 by using
[tex]\begin{gathered} \cos (180-\theta)=-\cos \theta \\ \Rightarrow\cos (180-\theta) \\ =-\cos 30 \end{gathered}[/tex]recall that
[tex]\begin{gathered} \cos 30=\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \cos 150=-\cos 30 \\ =-\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Therefore, the value of cos 150 is
[tex]-\frac{\sqrt[]{3}}{2}[/tex]
