Verify the identity. $\cot ^ { 2 } x - \cos ^ { 2 } x = \cot ^ { 2 } x \cos ^ { 2 } x$

Name: Verify the identity. $\cot ^ { 2 } x - \cos ^ { 2 } x = \cot ^ { 2 } x \cos ^ { 2 } x$
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\begin{aligned}\cot ^ { 2 } x - \cos ^ { 2 } x & = \frac { \cos ^ { 2 } x } { \sin ^ { 2 } x } - \cos ^ { 2 } x = \frac { \cos ^ { 2 } x - \sin ^ { 2 } x \cos ^ { 2 } x } { \sin ^ { 2 } x } = \frac { \cos ^ { 2 } x - \sin ^ { 2 } x \cos ^ { 2 } x } { \sin ^ { 2 } x } \& = \frac { \cos ^ { 2 } x \left( 1 - \sin ^ { 2 } x ight) } { \sin ^ { 2 } x } = \frac { \cos ^ { 2 } x \left( \cos ^ { 2 } x ight) } { \sin ^ { 2 } x } = \frac { \cos ^ { 4 } x } { \sin ^ { 2 } x } = \cot ^ { 2 } x \cos ^ { 2 } x\end{aligned}

Verify the Identity cot⁡2x−cos⁡2x=cot⁡2xcos⁡2x\cot ^ { 2 } x - \cos ^ { 2 } x = \cot ^ { 2 } x \cos ^ { 2 } xcot2x−cos2x=cot2xcos2x