Question

The number of solution of ${\sin }^{4}x-{\cos }^{2}x\sin x+2{\sin }^{2}x+\sin x=0$ in $0\le x\le 3\pi$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is B $4$

$si{n}^{4}x-co{s}^{2}x.sinx+2si{n}^{2}x+sinx=0$

$si{n}^{4}x-(1-si{n}^{2}x).sinx+2si{n}^{2}x+sinx=0$

$si{n}^{4}x+si{n}^{3}x+si{n}^{2}x=0$

$si{n}^{2}x(si{n}^{2}x+sinx+2)=0$

but $si{n}^{2}x+sinx+2$ can't be 0 because it's discriminant is negative,

thus $sinx=0$ is only solution

therefore in the given interval solution's are,

$x=0,\pi ,2\pi ,3\pi$