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) $\tan x$
B) $\cos \mathrm { x } \csc \mathrm { x }$
C) $\cot x$
D) $\frac { \cos x } { \sin x }$
E) $\frac { 1 } { \tan x }$

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)  $\tan x$
B)  $\cos \mathrm { x } \csc \mathrm { x }$
C)  $\cot x$
D)  $\frac { \cos x } { \sin x }$
E)  $\frac { 1 } { \tan x }$

Quizplus · Accepted Answer

The expression $\sin \left( \frac { \pi } { 2 } - x \right) \csc x$ simplifies to $\cos x \csc x$, which is equivalent to $\frac{1}{\sin x} \cos x$, or $\frac{\cos x}{\sin x}$. This is equivalent to $\cot x$ (C), which is also $\frac{1}{\tan x}$ (E), and directly given as $\frac{\cos x}{\sin x}$ (D). Option B is the same as the simplified expression. Option A, $\tan x$, is not equivalent to the given 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 $\sin \left( \frac { \pi } { 2 } - x \right) \csc x$