Is function x decreasing on (0, 2 )? - Vidyadip

Question

Is function $\cos x$ decreasing on $ (0, \frac{\pi}{2})$?

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Answer

Let $f_1(x) = \cos x$
$\therefore \mathrm{f}_{1}^{\prime}(\mathrm{x}) = -\sin x$
In interval $\left(0, \frac{\pi}{2}\right), \mathrm{f}_{1}^{\prime}(\mathrm{x}) = -\sin x < 0.$
Therefore $, f_1(x) = \cos x$ is strictly decreasing in interval $\left(0, \frac{\pi}{2}\right)$.

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