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

Answer

4

Explanation

`sin^(4)x- cos^(2) x sin x+2 sin^(2) x+ sin x=0`
or `sin x[sin^(3) x- cos^(2)x+2 sin x+1]=0`
or `sin x[ sin^(3)x+sin^(2) x+2 sin x]=0`
or `sin^(2) x [sin^(2) x+sin x+2]=0`
or `sin x=0`, where `x=0, pi, 2 pi, 3pi`
Hence, there are four solutions.