Question

Prove that the function f given by f (x) = log sin x is strictly increasing on (0,π/2) and strictly decreasing on (π/2,π).

Answer 1

Step-by-step explanation:

We have, f(x)=logsinx

∴f

′

(x)=

sinx

1

cosx=cotx

In interval (0,

2

π

),f

′

(x)=cotx>0.

∴ f is strictly increasing in (0,

2

π

).

In interval (

2

π

,π),f

′

(x)=cotx<0.

∴ f is strictly decreasing in (

2

π

,π).