Since, f(x)=cos2x is a trigonometric function and we know every trigonometric function is continuous.
⇒ f(x)= cos2x is continuous on [0,π].
Here, f’(x)= -2sin2x which exist in [0,π].
So, f(x)=cos2x is differentiable on (0,π).
Conditions of Rolle’s theorem are satisfied.
Hence, there exist at least one cϵ(0,π) such that f’(c)=0
i.e. -2sin2c =0
Thus, Rolle’s theorem is satisfied.
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