[tex]\begin{gathered} X(\frac{\pi}{3})cos(\frac{\pi}{6})=\frac{sin(\frac{\pi}{2})+sin(\frac{\pi}{6})}{2} \\ \\ X(\frac{\pi}{3})cos(\frac{\pi}{6})=\frac{1+\frac{1}{2}}{2} \\ \\ X(\frac{\pi}{3})cos(\frac{\pi}{6})=\frac{\frac{3}{2}}{2} \\ \\ X(\frac{\pi}{3})cos(\frac{\pi}{6})=\frac{3}{4} \\ \\ X(\frac{\pi}{3})(\frac{\sqrt{3}}{2})=\frac{3}{4} \\ \\ X(\frac{\pi}{3})=(\frac{3}{4})(\frac{2}{\sqrt{3}}) \\ \\ X(\frac{\pi}{3})=\frac{\sqrt{3}}{2} \\ \\ X=sin,\text{ because sin\lparen}\frac{\pi}{3}\text{\rparen=}\frac{\sqrt{3}}{2} \\ \\ Hence \\ \\ sin(\frac{\pi}{3})cos(\frac{\pi}{6})=\frac{s\imaginaryI n(\frac{\pi}{2})+s\imaginaryI n(\frac{\pi}{6})}{2} \end{gathered}[/tex]
