Simplify (csc(x)^2-1)sin(x)^2

$(\csc^{2} (x) - 1) \sin^{2} (x)$

Apply pythagorean identity.

$\cot^{2} (x) \sin^{2} (x)$

Rewrite $\cot (x)$ in terms of sines and cosines.

${(\frac{\cos (x)}{\sin (x)})}^{2} \sin^{2} (x)$

Apply the product rule to $\frac{\cos (x)}{\sin (x)}$ .

$\frac{\cos^{2} (x)}{\sin^{2} (x)} \sin^{2} (x)$

Cancel the common factor of $\sin^{2} (x)$ .

Cancel the common factor.

$\frac{\cos^{2} (x)}{\sin^{2} (x)} \sin^{2} (x)$

Rewrite the expression.

$\cos^{2} (x)$