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

Options

A. 3
B. 4
C. 5
D. 6

Answer

B

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-1+sin^(2) x+2 sin x+1]=0`
or `sin x [sin^(3)x+sin^(2) x+2 sin x]=0`
or `sin^(2) x=0 or sin^(2) x+sin x+2=0` (not possible for real x)
or `sin x=0`
Hence, the solutions are `x=0, pi, 2pi, 3pi`.