Question

How do you verify `cos^3 * sin^2 x = (sin^2 x - sin^4 x)cos x`?

Answer 1

See explanation

Explanation:

Note that `sin^2x + cos^2 x =1`
`implies cos^2x = 1-sin^2 x`

Now observe tht

`" L.H.S " = cos^3x * sin^2 x`
`= cos x * cos^2x * sin^2x`
`= cosx * (1- sin^2x) * sin^2x`
`= cosx*(sin^2x - sin^4x)`
`= (sin^2x - sin^4x)*cosx = " R.H.S "`