Can't make sense of this trig identity

[banfill_89]

Homework Statement

im in first year differential calculas and i have no idea what my prof wrote down...i just copied it and thought ide figure it out later. but i can't fore the life of me.

Homework Equations

the identitie that he wrote is:

sinC+sinB=2Sin (C+D)/2 cos (c-D)/2

The Attempt at a Solution

 

[banfill_89]

side note ) x+y = c
x-y = b

 

[banfill_89]

i understand where the sin C + sin B, its the (c+d)/2 that has me confused...these identities are just another way of writing the identities derived from adding and subtracting the addition and subtraction identities

 

[Dick]

Change the 'D' to 'B'. Then it works. Sure, it's derived from addition and subtraction identities. Basically everything is.

 

[banfill_89]

where did the (c+b)/2 come from...i know they subbed that in for x...but why?

 

[Dick]

I don't know, you didn't give us the whole problem. I do know sin(c)+sin(b)=2*sin((c+b)/2)*cos((c-b)/2).