Show that the function given by $f (x) = s i n x$ is

strictly decreasing in $(\frac{π}{2}, π)$

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Solution

Since, for each $x ϵ (\frac{π}{2}, π), c o s x < 0$ ; we have f'(x)<0
( $∵$ cos x in IInd quadrant is negative)
Hence, f is strictly decreasing on $(\frac{π}{2}, π)$ .

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