Final answer:
To simplify sinxcos^2x-sinx, factor out sinx and apply a trigonometric identity, resulting in the simplified expression -sin^3x.
Step-by-step explanation:
The question deals with the simplification of a trigonometric expression.
To simplify sin(x)cos2(x) - sin(x), we can factor out a common factor of sin(x), which gives us sin(x)(cos2(x) - 1).
Using a trigonometric identity, cos2(x) - 1 can be rewritten as -sin2(x).
This leads to the simplification sin(x)(-sin2(x)), which simplifies further to -sin3(x).