ok this come from

sin(a+b) = sina cosb + sinb cosa

sin(a-b) = sina cosb - sinb cosa

find the sum of two

sin(a+b) + sin(a-b) = 2 sina cosb

let a+b = x and a-b =y ..........

solve this ( find the value of a , b with respect of x .y )

a = (x+y)/2

b = (x-y)/2

now we have

sinx + siny =2 sin((x+y)/2) cos ((x-y)/2)

finish