Question

The total number of solutions of $\ln \left|\sin x\right|=-x^2+2x$ in $[-\frac{\pi }{2},\frac{3\pi }{2}]$ is equal to

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

Answer 1

The correct option is B 2

$\ln \mid \sin x\mid =-x^2+2x$, $x\in [-\frac{\pi }{2},\frac{3\pi }{2}]$

By plotting graph of $y=\ln \mid \sin x\mid$ and $y=-x^2+2x$

it can be easily seen that both curve intersect two times in the given interval,
thus given equation has two solution.