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Prove that the function f given by f(x)=logsinx is strictly increasing on (0,pi/2) and strictly decreasing on (pi/2,pi)
Applications of Derivatives | CBSE | Class 12 | Exercise 6.2 | Maths | NCERT
Prove that the function f given by f(x)=logsinx is strictly increasing on (0,pi/2) and strictly decreasing on (pi/2,pi)

Given: 

 

On the interval  i.e., in first quadrant,

 > 0

Therefore,  is strictly increasing on .

On the interval  i.e., in second quadrant,

 < 0

Therefore,  is strictly decreasing on .

i

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