The sine addition formula states that
[tex]\sin (a+b)=\sin a\cos b+\cos a\sin b[/tex]
Thus, in our case,
[tex]\sin (x+y)=\sin x\cos y+\cos x\sin y[/tex]
Then,
[tex]\begin{gathered} \Rightarrow\sin x\cos y+\cos x\sin y=\frac{1}{2}\sin x+\frac{\sqrt[]{3}}{2}\cos x \\ \Rightarrow\cos y=\frac{1}{2},\sin y=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]
Solving for y,
[tex]\Rightarrow y=\cos ^{-1}(\frac{1}{2})=\frac{\pi}{3}[/tex]
Thus, the answer is y=pi/3
