Question

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

• A. $0$
• B. $5$
• C. $6$
• D. $10$

Answer 1

The correct option is C $6$

We have, $3{\sin }^{2}x-7\sin x+2=0$
$\Rightarrow (3\sin x-1)(\sin x-2)=0$
$\Rightarrow \sin x=\frac{1}{3}$ $[\because \sin x-2\ne 0]$
$\Rightarrow x={\sin }^{-1}\frac{1}{3},\pi -{\sin }^{-1}\frac{1}{3},2\pi +{\sin }^{-1}\frac{1}{3},3\pi -{\sin }^{-1}\frac{1}{3},4\pi +{\sin }^{-1}\frac{1}{3},5\pi -{\sin }^{-1}\frac{1}{3}$.