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

Question

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

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Answer

Let f₁(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, f₁(x) = cos x is strictly decreasing in interval $\left(0, \frac{\pi}{2}\right)$.

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