Since, f(x)=sinx+cosx is a trigonometric function and we know every trigonometric function is continuous.
⇒ f(x)= sinx+cosx is continuous on .
Here, f’(x)= cosx-sinx which exist in .
So, f(x)= sinx+cosx is differentiable on
Conditions of Rolle’s theorem are satisfied.
Hence, there exist at least one such that f’(c)=0
i.e. cosc-sinc =0
Thus, Rolle’s theorem is satisfied.
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