Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1$
A) $\frac { 1 + \cos ^ { 2 } x } { \sin }$
B) $\cos ^ { 2 } x ( 1 - \sin x )$
C) $\frac { \cos ^ { 4 } x } { 1 + \sin x }$
D) $\cos ^ { 2 } x - \cos ^ { 2 } x \sin x$
E) $\frac { 1 - \sin x } { \sec ^ { 2 } x }$

Question

Factor;then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1$ ​
A)​ $\frac { 1 + \cos ^ { 2 } x } { \sin }$
B)​ $\cos ^ { 2 } x ( 1 - \sin x )$
C)​ $\frac { \cos ^ { 4 } x } { 1 + \sin x }$
D)​ $\cos ^ { 2 } x - \cos ^ { 2 } x \sin x$
E)​ $\frac { 1 - \sin x } { \sec ^ { 2 } x }$

Quizplus · Accepted Answer

The given expression $\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1$ can be factored and simplified using trigonometric identities, but none of the provided options directly matches this expression when simplified correctly. However, option A, when simplified, does not match the original expression's simplified form, making it the correct choice by process of elimination and considering the question asks for the option that is not equivalent.

Factor;then Use Fundamental Identities to Simplify the Expression Below and Determine