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

Prove that the function `f` given by `f(x)=logcosx` is strictly increasing on `(-pi//2,\ 0)` and strictly decreasing on `(0,\ pi//2)` .

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We have given
`f(x)=logcosx`
Then we have to show that `f(x)` is strictly increasing on `(-pi/2,0)` and strictly decreasing on `(0,pi/2)`
Then
`f(x)=logcosx`
Differentiate this w.r.t `x`
`f'(x)=(-sinx)/(cosx)=-tanx`
...
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