Answer
Identity is verified.
$cos^3~x~sin^2x=(sin^2x-sin^4x)cos~x$
Work Step by Step
We know that:
$sin^2x+cos^2x=1$
$cos^2x=1-sin^2x$
Start at the right side of the equation:
$(sin^2x-sin^4x)cos~x=sin^2x(1-sin^2x)cos~x=sin^2x(cos^2x)cos~x=sin^2x~cos^3~x$
