Prove that the function given by $f (x) = cos x$ is strictly decreasing in $(0, π)$ .

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Solution

Given $f (x) = cos x$
$\frac{d}{d x} f (x) = - sin x$
in $(0, π), sin x > 0$
$∴$ in $x ϵ (0, π); f^{^{'}} (x) < 0$
Hence $f (x)$ is strictly decreasing .

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