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