Factor; Then Use Fundamental Identities to Simplify the Expression Below $$\cot ^ { 2 } \alpha - \cot ^ { 2 } \alpha \cos ^ { 2 } \alpha$$

question 96

Multiple Choice

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
$$\cot ^ { 2 } \alpha - \cot ^ { 2 } \alpha \cos ^ { 2 } \alpha$$

• A) \(\cos ^ { 2 } \alpha\)
• B) \(1 - \sin ^ { 2 } \alpha\)
• C) \(\tan ^ { 2 } \alpha\)
• D) \(\sin ^ { 2 } \left( \frac { \pi } { 2 } - \alpha \right)\)
• E) \(\frac { 1 } { \sec ^ { 2 } \alpha }\)

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Definitions:

Linguistic Determinism

The concept that language determines or significantly influences thought patterns and perceptions of the world.

Language Acquisition

The process by which humans gain the ability to perceive and comprehend language, as well as to produce and use words and sentences to communicate.

Insight Theory

A psychological theory suggesting that problem-solving can sometimes happen suddenly through understanding the relationships between various parts of a problem rather than through trial and error.

Language On Thinking

The influence of language on cognitive processes and the way individuals conceptualize the world.