
Given, sin x + sin y + sin z = 3
Now, whatever the value of x, y and z, the value of sign function always lie in the interval [-1, 1]
So, sin x + sin y + sin z = 3 is possible only when sin x = sin y = sinz = 1
=> sin x = sin y = sinz = sin 90
=> x = y = z = 90
So, cos x + cos y + cos z = cos 90 + cos 90 + cos 90 = 0