Question

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

• A. 0
• B. 5
• C. 6
• D. 10

Answer 1

The correct option is C 6

$3si{n}^{2}x-7sinx+2=0$

$\Rightarrow 3si{n}^{2}x-sinx-6sinx+2=0$

$\Rightarrow sinx(3sinx-1)-2(3sinx-1)=0$

$\Rightarrow (3sinx-1)(sinx-2)=0$

$\Rightarrow sinx=\frac{1}{3},sinx=2$

but $-1\le sinx\le 1$

so only solution is,

$sinx=\frac{1}{3}=sin\alpha$, where $\alpha =si{n}^{-1}\left(\frac{1}{3}\right)$

Hence general solution is,

$x=n\pi +(-1{)}^n\alpha$

In [$0,5\pi$] solution is $x=\alpha ,\pi -\alpha ,2\pi +\alpha ,3\pi -\alpha ,4\pi +\alpha ,5\pi -\alpha$