csc A - sin A to cos A cot A
and
sin A cot^2 A (sec - 1) to sin A
$\displaystyle \csc(A) - \sin(A) = \frac{1}{\sin(A)} - \sin(A) $
$\displaystyle = \frac{1}{\sin(A)} - \frac{\sin^2(A)}{\sin(A)} $
$\displaystyle = \frac{\cos^2{A}}{\sin(A)} = \frac{\cos(A) \times \cos(A)}{\sin(A)} $
$\displaystyle = \frac{\cos(A)}{\sin(A)} \times \cos(A) $
Consider the identity:
$\displaystyle \sin^2(A) + \cos^2(A) = 1 $
Divide it by $\displaystyle \cos^2(A) $
$\displaystyle \tan^2(A) + 1 = \sec^2(A) $
$\displaystyle \sec^2(A) - 1 = \tan^2(A) $
Hence your problem becomes:
$\displaystyle \sin(A) \cot^2(A) \tan^2(A) $
And you know that $\displaystyle \tan^2(A) = \frac{1}{\cot^2(A)}$
Does that help?