Add or Subtract as Indicated; Then Use Fundamental Identities to Simplify

question 10

Multiple Choice

Add or subtract as indicated; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.
$$\sin x + 1 + \frac { 1 } { \sin x - 1 }$$

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

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