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

question 10

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:

Budget Deficits

The condition when a government, organization, or individual spends more money than it receives over a certain period, requiring borrowing to bridge the gap.

Multiplier Effect

An economic phenomenon where an initial injection of spending leads to increased income and consumption, further amplifying the initial economic impact.

Aggregate Demand

The total demand for all goods and services in an economy at a given overall price level and within a specified period.

National Income

The total income earned by a nation's people and businesses, including wages, rent, interest, and profits.