Which of the following expressions is equivalent to $\frac { 5 \cot ^ { 2 } t } { \csc t }$
(t $\neq$ $\pi$n, where n is a whole number)
A) $\frac { 5 - 5 \sin ^ { 2 } t } { \sin t }$
B) $\frac { - 1 - \sin ^ { 2 } t } { 5 \sin t }$
C) $\frac { 5 - 5 \cos ^ { 2 } t } { \cos t }$
D) $\frac { 5 + 5 \sin ^ { 2 } t } { \sin t }$
E) $\frac { 5 + 5 \cos ^ { 2 } t } { \cos t }$

Question

Which of the following expressions is equivalent to $\frac { 5 \cot ^ { 2 } t } { \csc t }$ 
 (t $\neq$  $\pi$n, where n is a whole number)  
A)  $\frac { 5 - 5 \sin ^ { 2 } t } { \sin t }$
B) $\frac { - 1 - \sin ^ { 2 } t } { 5 \sin t }$
C) $\frac { 5 - 5 \cos ^ { 2 } t } { \cos t }$
D) $\frac { 5 + 5 \sin ^ { 2 } t } { \sin t }$
E) $\frac { 5 + 5 \cos ^ { 2 } t } { \cos t }$

Quizplus · Accepted Answer

The expression $\frac { 5 \cot ^ { 2 } t } { \csc t }$ can be simplified using trigonometric identities. $\cot^2t = \frac{1}{\sin^2t}$ and $\csc t = \frac{1}{\sin t}$, so the expression becomes $\frac{5}{\sin^3t}$. Using the Pythagorean identity $\sin^2t + \cos^2t = 1$, we can rewrite $\cot^2t$ as $\frac{1 - \sin^2t}{\sin^2t}$, leading to the equivalent expression $\frac { 5 - 5 \sin ^ { 2 } t } { \sin t }$.

Which of the Following Expressions Is Equivalent To 5cot⁡2tcsc⁡t\frac { 5 \cot ^ { 2 } t } { \csc t }csct5cot2t​

Which of the Following Expressions Is Equivalent To $\frac { 5 \cot ^ { 2 } t } { \csc t }$