Question

___pi/3 cos pi/6=1/2 (sin pi/2 + sin pi/6)

Answer 1

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