hey friend in which interval u r talking abt?

we get f^'(x)= 1+cos x which if >= 0 will be only increasing and if only >0 then it will be strictly increasing

hope u got it..........

it is increasing as if you plot its graph it would be a sine curve around y=x line and whose keeps on incresing and decreasing but if you view function as a whole increases in its value hence it is increasing not strictly increasing.

f'(x)>0 for strictly increasing and f'(x)0 for increasing