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Question
Prove that the function f given by f(x) = log sin x is strictly increasing on `(0, pi/2)` and strictly decreasing on `(pi/2, pi)`
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Solution
We have, f (x) = log (sin x)
Differentiating w.r.t x, we get
`f' (x) = 1/ (sin x) (cos x) = cot x`
As cot x >0 for all `x in (0, pi/2)` and cot x < 0
For all `x in (pi/2, pi),` Therefore, f (x) is strictly increasing on `(0, pi/2)` and strictly decreasing on `(pi/2, pi).`
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