Q. 193.5( 2 Votes )
Verify Rolle’s th
Since, f(x) = sinx-sin2x is a trigonometric function and we know every trigonometric function is continuous.
⇒ f(x) = sinx-sin2x is continuous on [0,2π].
Here, f’(x)= cosx-2cos2x which exist in [0,2π].
So, f(x)= sinx-sin2x is differentiable on (0,2π)
Here, f(0)= sin0-sin0 = 0
And f(2π)=sin(2π)-sin(4π) =0
Conditions of Rolle’s theorem are satisfied.
Hence, there exist at least one cϵ(0,2π) such that f’(c)=0
i.e. cosx-2cos2x =0
i.e. c=32° 32’ or c=126°23’
Value of c=32°32’ϵ(0,2π)
Thus, Rolle’s theorem is satisfied.
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