(Originais Teachy 2023) - Question Medium of Mathematics

João is studying the properties of trigonometric functions and is interested in the applications of the Prostaférese Formulas. He found the following expression: sin(x)cos(y) + cos(x)sin(y). (a) Apply the Prostaférese Formula to transform João's expression into a sum or subtraction of trigonometric functions. (b) Use the simplified expression obtained in the previous item to calculate the value of the expression when x = 60° and y = 30°. (c) Suppose João wants to use the inverse Prostaférese Formula to return to the original expression given by the products of trigonometric functions. Show how João can use the inverse formula and check if the values obtained in items (a) and (b) remain consistent.