Question

How do you Solve 3sinxcos^2x+sin^3x=sinx ?

Answer 1

`x = n pi/2,qquad n in ZZ`

Explanation:

`3sinxcos^2x+sin^3x=sinx implies`
`sinx(3cos^2x+sin^2x) - sinx=0 implies`
`sinx(3cos^2x+sin^2x-1)=0 implies`
`sinx(3cos^2x-cos^2 x) = 0 implies`
`2sin x cos^2 x = 0`

So, either `sin x = 0` or `cos x = 0`. This means that `x` must be a integer multiple of `pi/2`.