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:

Road To Serfdom

A book by Friedrich Hayek, published in 1944, warning of the potential dangers of government control leading to totalitarianism, arguing for the preservation of individual freedoms.

Laissez-Faire Economics

An economic philosophy of free-market capitalism that opposes government intervention.

Austrian-Born Economist

Refers to economists originating from Austria, particularly those associated with the Austrian School of Economics, known for emphasizing the importance of individual choice and spontaneous order in the economy.

Nazi Germany

The regime led by Adolf Hitler and the National Socialist German Workers' Party from 1933 to 1945, characterized by its totalitarian government and pursuit of aggressive expansion.