Trigonometric Ratio question

Consider the equation **2 Sin x cos y** **= sin ( x + y ) + sin ( x - y ).**

Emilio claims that substituting **x = 5pi/4 **and **y = 3pi/4** makes the equation true.

a) Determine an exact value for the left side using Emilio's solution.

b) Determine an exact value for the right side using Emilio's solution.

c) Is Emilio correct?

d) Is **x = 5pi/6** and **y = pi/6** a solution? Justify your answer.

e) Based on the answers to parts c) and d), is it reasonable to conclude that the equation is true no matter what angles are substituted for **x** and **y**? Justify your answer.