Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.
$\sin \left( \frac { \pi } { 2 } - x \right) \csc x$
A) -1
B) $\frac { \cos x } { \sin x }$
C) cot x
D) 1/ tan x
E) cos x csc x

Question

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. 
 $\sin \left( \frac { \pi } { 2 } - x \right) \csc x$  
A) -1
B)  $\frac { \cos x } { \sin x }$
C) cot x
D) 1/ tan x
E) cos x csc x

Quizplus · Accepted Answer

The expression $\sin \left( \frac { \pi } { 2 } - x \right)$ is equivalent to $\cos x$ due to the co-function identity. Thus, the expression simplifies to $\cos x \csc x = \frac{\cos x}{\sin x}$, which is equivalent to $\cot x$ and $\frac{1}{\tan x}$. The expression $\cos x \csc x$ is also equivalent. However, -1 is not equivalent to the simplified expression.

Use Fundamental Identities to Simplify the Expression Below and Then sin⁡(π2−x)csc⁡x\sin \left( \frac { \pi } { 2 } - x \right) \csc xsin(2π​−x)cscx

Use Fundamental Identities to Simplify the Expression Below and Then $\sin \left( \frac { \pi } { 2 } - x \right) \csc x$