Show that the following identity holds for all real α and β:
a. (i) Starting from the left-hand side, convert the product sin(α+β)cos(α−β) to a single trigonometric function of one angle.
b. (ii) Similarly convert the product cos(α+β)sin(α−β) to a single trigonometric function of one angle.
c. (iii) Hence prove that
sin(α+β)cos(α−β)+cos(α+β)sin(α−β)=sin2α.