Question

The function log sin x is decreasing in $[\frac{\pi }{2},\pi ]$

• A. True
• B. False

Answer 1

The correct option is A True

$f\left(x\right)=\log \left(\sin x\right)$

$f^{\prime }\left(x\right)=\frac{1}{\sin x}\times \cos x$

$=\cot x$

$\Rightarrow f^{\prime }\left(x\right)=0$

$\Rightarrow \cot x=0$

$x=\frac{\pi }{2},\frac{3\pi }{2}$

Since,

$f^{\prime }\left(x\right)<0\text{in}[\frac{\pi }{2},\pi ]$

Hence, It must be decreasing.