Prove the Identity $$\csc ^ { 3 } x \tan ^ { 2 } x = \csc x \left( 1 + \tan ^ { 2 } x \right)$$

question 110

Essay

Prove the identity.
- $$\csc ^ { 3 } x \tan ^ { 2 } x = \csc x \left( 1 + \tan ^ { 2 } x \right)$$

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Definitions:

Learned Helplessness

A condition in which a person suffers from a sense of powerlessness, arising from a traumatic event or persistent failure to succeed, characterized by a lack of initiative, effort, or persistence.

Latent Learning

Learning that occurs without any obvious reinforcement and is not demonstrated until there is an incentive to perform.

Insight Learning

A cognitive process where an individual suddenly realizes how to solve a problem without trial-and-error, often seen as a form of intuitive understanding.

Punishment By Removal

The punishment of a response by the removal of a pleasurable stimulus.