Given the expression:
[tex]sin(x+y)=\frac{\sqrt{3}}{2}sinx+\frac{1}{2}cosx[/tex]
You need to remember the following Trigonometric Identity:
[tex]sin(x+y)=sinx\cdot cosy+cosx\cdot siny[/tex]
In this case, you can identify that:
[tex]\begin{gathered} cosy=\frac{\sqrt{3}}{2} \\ \\ siny=\frac{1}{2} \end{gathered}[/tex]
By definition:
[tex]\begin{gathered} cos(\frac{\pi}{6})=\frac{\sqrt{3}}{2} \\ \\ sin(\frac{\pi}{6})=\frac{1}{2} \end{gathered}[/tex]
Hence, you can determine that:
[tex]y=\frac{\pi}{6}[/tex]
Therefore, the answer is: Last option.
