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Verifying trigonometric identity: Complete the proof of the identity by choosing the rule that justifies each step tanx( csc(sqaured)x-1)=cotx If I break this down I

Verifying trigonometric identity:

Complete the proof of the identity by choosing the rule that justifies each step

tanx( csc(sqaured)x-1)=cotx

If I break this down I come up with

tanx(cot(squared)x) which would be pythagorean

tanx.cotx.cotx which would be algebra

tanx(1/tanx)cotx which would also be algebra

cotx which would be quotient

Am I correct with my identities?

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