Question

The number of solutions of the equation $(|\sin x|-1)(5|\sin x|-1)=0$ in $[0,2\pi ]$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is D $6$

$(|\sin x|-1)(5|\sin x|-1)=0$
$\Rightarrow |\sin x|=1\text{or}|\sin x|=\frac{1}{5}$
So, plotting the graphs of $y=|\sin x|,y=1,y=\frac{1}{5}$


$\therefore$ From the above graph, we conclude that the total number of solutions of the given equation is $6.$