Refection #21 I Think

NO SCHOOL TOMORROW!!!!!!!!!! It's about time we get a day off, Lutcher is already on like their third day of no school since the holidays ended. This week was really easy. I'm not gunna lie though, I think it's probably because I did my homework everyday this week for the first time this year. The formulas I think I picked up the best were the Tan. formulas:
Tan (α + β)=tan α + tan β/1-tan α tan β
Tan (α - β)=tan α - tan β/1+tan α tan β

Say you get tan 15degrees
You would use two angles from the trig chart that add or subtract to get 15 degrees (45 and 30). You plug them into the α & β parts of the problem then solve it. So here is what you would get.

Tan (45 - 30)=tan 45 - tan 30/1+tan 45 tan 30
=tan √2/2- tan√3/3 /1+tan √2/2 tan√3/3
=3(√3-3)/3(√3+3)
=(√3-3)/(√3+3)

The only thing I really dont understand from this week is the four random formulas we wrote down but never used.
Sin x + sin y= 2 sin x + y/2 cos x-y/2
Sin x - sin y= 2 cos x + y/2 sin x-y/2
Cos x + cos y= 2 cos x + y/2 cos x-y/2
Cos x - cos y= 2 sin x + y/2 sin x-y/2
What is this????