Factor; Then Use Fundamental Identities to Simplify the Expression Below $$\csc ^ { 3 } x - \csc ^ { 2 } x - \csc x + 1$$

question 12

Multiple Choice

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
$$\csc ^ { 3 } x - \csc ^ { 2 } x - \csc x + 1$$

• A) \(\csc x \cot ^ { 2 } x - \cot ^ { 2 } x\)
• B) \(\cos ^ { 2 } x \left( \frac { 1 - \sin x } { \sin ^ { 3 } x } \right)\)
• C) \(\frac { \cos ^ { 4 } x } { \sin ^ { 3 } x + \sin ^ { 4 } x }\)
• D) \(\frac { 1 - \sin x - \sin ^ { 2 } x + \sin ^ { 3 } x } { \sin ^ { 3 } x }\)
• E) \(\frac { \sec ^ { 2 } x + \tan ^ { 2 } x } { \csc x }\)

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Definitions:

Instrument Decay

The phenomenon where measurement tools or instruments become less accurate over time due to usage, age or environmental conditions.

Human Observers

Individuals who watch and record behaviors or phenomena in research settings, often used for qualitative data collection.

Measurement

The process of quantifying or qualitatively assessing variables, objects, or events.

Fatigued

The state of being extremely tired, exhausted, or weary from physical or mental exertion.