Question

use the angle sum identity to find the exact value of each: cos 105°

Answer 1

You need to know the equation for cos(a+b)=?
and then know what
cos(30)
cos(60)
cos(45)
and probably the sin()s as well.

Answer 2

cos(a+b) = cos(a)cos(b)-sin(a)sin(b)
so if you take 105=60 + 45 then you have
cos(60+45) = cos(60)cos(45)-sin(60)sin(45)