Answer :

Condition (1):


Since, f(x)=cosx is a trigonometric function and we know every trigonometric function is continuous.


f(x)=cosx is continuous on .


Condition (2):


Here, f’(x)=-sinx which exist in .


So, f(x)=cosx is differentiable on .


Condition (3):


Here,


And


i.e.


Conditions of Rolle’s theorem are satisfied.


Hence, there exist at least one such that f’(c)=0


i.e. -sinc=0


i.e. c=0


Value of


Thus, Rolle’s theorem is satisfied.


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