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

question 34

Multiple Choice

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

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

---

Definitions:

Habituation

The process of becoming accustomed to a stimulus after repeated exposure, leading to a decrease in the response to that stimulus over time.

Dishabituation

The renewal of attention or response to a novel stimulus after habituation has occurred to a previous stimulus.

Sensation

The method through which our sensory organs and nervous system capture and interpret energy from stimuli in our surroundings.

Perception

The process by which individuals interpret sensory information to understand their environment.