**We know that the cos function attains its minimum value as -1 at π radians.**

- So, x = y = π
- x + y = 2π Now, we can write as;
- cos(x + y) = cos 2π = 1
**This is the min value of** cos(x + y).

Thus, the minimum value of cos x + cos y + cos (x + y) = -1 + (-1 ) +1 = -1

Also, we know that cos function attains its max value 1 at 0 radians.

so, x = y = 0

Hence, the maximum value of cos x + cos y + cos (x + y) = 1 + (1 )+1 = 3

**Thus, the maximum value of cos x + cos y + cos (x + y) = 3 and minimum value = -1**