Use Fundamental Identities to Simplify the Expression Below and Then $\cos \alpha ( \sec \alpha - \cos \alpha )$

question 41

Multiple Choice

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\cos \alpha ( \sec \alpha - \cos \alpha )$

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

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Definitions:

Hot Magma

Molten or partially molten rock beneath the Earth's surface, from which igneous rocks are formed.

Subduction

Subduction is a geological process in which one tectonic plate moves under another plate and into the mantle as the plates converge, typically occurring at oceanic trenches.

Juan de Fuca Ridge

A tectonic plate boundary located off the coast of the Pacific Northwest region of North America, characterized by seafloor spreading and volcanic activity.

Hot Spot

A region with significantly higher temperature than its surroundings, often related to volcanic activity or environmental anomalies.