Question

The total number of solutions of ${\log }_e|\sin x|=-x^2+2x$ in $[0,\pi ]$ is equal to

• A. $1$
• B. $2$
• C. $4$
• D. None of these

Answer 1

The correct option is A $1$

Let $f\left(x\right)=\log \sin xxϵ[0,\pi ]$

let $g\left(x\right)=-x^2+2x$

$g^{\prime }\left(x\right)=-2x+2$ now since $xϵ[0,\pi ]$

$g^{\prime }\left(x\right)=0x=1$

max value of $g\left(x\right)=g\left(1\right)=2-1=1$