Question

How do you simplify the expression `sint-sintcos^2t`?

Answer 1

`sin t - sin t cos^2 t=sin^3 t`

Explanation:

Note that `sin^2 t + cos^2 t = 1` for any `t`

Hence `1-cos^2 t = sin^2 t`

So we find:

`sin t - sin t cos^2 t`

`=sin t (1 - cos^2 t)`

`=sin t sin^2 t`

`=sin^3 t`