Question

The number of values of x in the interval $[0,5\pi ]$ satisfying the equation $3{\sin }^{2}x-7\sin x+2=0$ is

• A. 5
• B. 6
• C. 10

Answer 1

The correct option is B 6

$3{\sin }^{2}x-7\sin x+2=0$
or $(\sin x-2)(3\sin x-1)=0$
$\Rightarrow \sin x=\frac{1}{3}=\sin \alpha \text{(say)}(\sin x=2\text{is not possible)}$
There exists two values in$(0,\pi ),(2\pi ,3\pi )\text{and}(4\pi ,5\pi ).$
Hence there are six solutions