Simplify (1-cos(x)^2)cot(x)^2

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Trigonometry

$(1 - \cos^{2} (x)) \cot^{2} (x)$

Apply pythagorean identity.

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

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

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

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

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

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

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Cancel the common factor.

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

Rewrite the expression.

$\cos^{2} (x)$

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