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Prove that the function f given by f(x) ...

Prove that the function f given by `f(x) = log | cos x|" is decreasing on "(0,pi/2)" and increasing on "((3pi)/2,2pi)`.

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f(x) = log cos x
` rArr f'(x) = (-sin x)/(cos x) =- tan x`
(a) For strictly decreasing function
`f'(x) lt 0`
` rArr -tan x lt 0`
` rArr tan x gt 0`
` rArr x in ]0,pi/2[`
(b) For strictly decreasing function
` f'(x) gt 0`
` rArr - tan x gt 0`
` rArr tan x lt 0`
` rArr x in ]pi/2, pi [`
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