Prove the Identity $$\frac { \cot ^ { 2 } x } { \csc x + 1 } = \frac { 1 - \sin x } { \sin x }$$

question 79

Essay

Prove the identity.
- $$\frac { \cot ^ { 2 } x } { \csc x + 1 } = \frac { 1 - \sin x } { \sin x }$$

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Definitions:

Psychosis

A mental disorder where thought and emotions are so impaired that contact is lost with external reality.

Paranoia

A psychological state in which individuals experience false beliefs of being persecuted, unnecessary feelings of jealousy, or an inflated sense of self-worth.

Depression

A mental health disorder marked by persistent feelings of sadness, hopelessness, and a lack of interest or pleasure in activities.

Psychosomatic

Referring to physical symptoms that are caused or significantly influenced by psychological factors, such as stress or anxiety.