The extreme values of the function f(x) = sin x + cos x are required for values of x that lie in the interval [pi/2, pi]
f'(x) = cos x - sin x
cos x - sin x = 0
=> cos x = sin x
This is true for x = pi/4 but pi/4 does not lie in the given interval.
In the given interval the graph is moving downwards uniformly.
Its highest value is 1 and the lowest value is -1
The extreme values of f(x) = sin x + cos x for x in [pi/2, pi] are 1 and -1