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# Find the intervals in which f(x) = logcosx is strictly decreasing and strictly increasing.

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Toolbox:
• For strictly decreasing $f ' (x) < 0$
• For strictly increasing $f ' (x) > 0$
$f'(x) = -tan\:x$
is positive in $\bigg( \large\frac{\pi}{2}\: \pi \bigg) \cup \bigg( \large\frac{3\pi}{2}\: 2\pi \bigg)$ and hence is increasing.
and is decreasing in $\bigg( 0 \: \large\frac{\pi}{2} \bigg) \cup \bigg( \pi \: \large\frac{3\pi}{2} \bigg)$
answered Apr 13, 2013