Add or Subtract as Indicated; Then Use Fundamental Identities to Simplify

question 77

Multiple Choice

Add or subtract as indicated; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
$\sin x + 1 + \frac { 1 } { \sin x - 1 }$

• A) \(\frac { \sin ^ { 2 } x } { \sin x - 1 }\)
• B) \(\frac { 1 - \cos ^ { 2 } x } { \sin x - 1 }\)
• C) \(\frac { 1 + \cos ^ { 2 } x } { \sin x - 1 }\)
• D) \(\frac { \sec x - \cos x } { \tan x - \sec x }\)
• E) \(\frac { \csc x - \cot x \cos x } { 1 - \csc x }\)

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Definitions:

Episodic Memories

A type of long-term memory that involves the recollection of specific events, situations, and experiences, including the contexts and emotions associated with them.

Temporal Lobes

Regions of the cerebral cortex located beneath the temples, involved in processing auditory information and encoding memory.

Hippocampus

A major component of the brain located in the temporal lobe, critical for the storage of new memories and is associated with learning and emotions.

Long-Term Memories

Long-Term Memories are memories that can last from days to decades, involving the storage and retrieval of information over an extended period.