Use the fundamental identities to write the first expression in terms of the second. $\tan ^ { 2 } t \sec t , \cos t$
A) $\frac { 1 - \cos ^ { 2 } t } { \cos ^ { 3 } t }$

B) $\frac { 1 } { \cos t }$

C) $\frac { 1 + \cos ^ { 2 } t } { \sqrt { 1 - \cos t } }$

D) $\frac { \cos ^ { 2 } t - 1 } { \cos ^ { 3 } t }$

E) $\frac { 1 } { \cos ^ { 3 } t }$

Question

Use the fundamental identities to write the first expression in terms of the second. $\tan ^ { 2 } t \sec t , \cos t$
A) $\frac { 1 - \cos ^ { 2 } t } { \cos ^ { 3 } t }$

B) $\frac { 1 } { \cos t }$

C) $\frac { 1 + \cos ^ { 2 } t } { \sqrt { 1 - \cos t } }$

D) $\frac { \cos ^ { 2 } t - 1 } { \cos ^ { 3 } t }$

E) $\frac { 1 } { \cos ^ { 3 } t }$

Quizplus · Accepted Answer

Using the identity $\tan^2t = \frac{\sin^2t}{\cos^2t}$ and $\sec t = \frac{1}{\cos t}$, we can rewrite $\tan^2t \sec t$ as $\frac{\sin^2t}{\cos^2t} \cdot \frac{1}{\cos t} = \frac{\sin^2t}{\cos^3t}$. Since $\sin^2t = 1 - \cos^2t$, the expression becomes $\frac{1 - \cos^2t}{\cos^3t}$.

Use the Fundamental Identities to Write the First Expression in Terms