Function f(x) = cos x − 2 λ x is monotonic decreasing when

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f\left( x \right) = \cos x - 2 \lambda x f'\left( x \right) = - \sin x - 2 \lambda \text { For f(x) to be decreasing, we must have } f'\left( x \right) < 0 \Rightarrow - \sin x - 2 \lambda < 0 \Rightarrow sin x + 2 \lambda > 0 \Rightarrow 2 \lambda > - \sin x \text { We know that the maximum value of -sin x is 1 }. \Rightarrow 2 \lambda > 1 \Rightarrow \lambda > $\frac{1}{2}$

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