Find all the solution of `4co s^2xsinx-2sin^2x=3sinx`

Answer

`x=n pi` or `x=n pi+(-1)^(n)(pi)/(10)` or `x =n pi+(-1)^(n)(-(3pi)/(10))`

Explanation

`4cos^(2)x sin x-2 sin^(2)x=3 sin x`
`rArr 4(1-sin^(2)x)sin x - 2 sin^(2)x-3 sin x =0`
`rArr sin x (4-4 sin^(2)x-2 sin x-3) =0`
`rArr sin x (4sin^(2)x +2 sin x-1)=0`
`rArr sin x = 0` or `4 sin^(2) x+2 sin x -1 =0`
`rArr x = n pi, n in Z` or `x = (sqrt(5) -1)/(4), (-(sqrt(5)+1))/(4)`
`rArr x = n pi` or `x = n pi +(-1)^(n)(pi)/(10)` or `x = n pi +(-1)^(n)(-(3pi)/(10)), n in Z`