Write the following as an algebraic expression in u, u 0.
-$\tan \left( \operatorname { arcsec } \frac { \sqrt { \mathrm { u } ^ { 2 } + 25 } } { \mathrm { u } } \right)$
A) $5 \mathrm { u }$
B) $\frac { u \sqrt { u ^ { 2 } + 25 } } { u ^ { 2 } + 25 }$
C) $\frac { \sqrt { u ^ { 2 } + 5 } } { u ^ { 2 } + 5 }$
D) $\frac { 5 } { u }$

Question

Write the following as an algebraic expression in u, u > 0.
-$\tan \left( \operatorname { arcsec } \frac { \sqrt { \mathrm { u } ^ { 2 } + 25 } } { \mathrm { u } } \right)$
A) $5 \mathrm { u }$
B) $\frac { u \sqrt { u ^ { 2 } + 25 } } { u ^ { 2 } + 25 }$
C) $\frac { \sqrt { u ^ { 2 } + 5 } } { u ^ { 2 } + 5 }$
D) $\frac { 5 } { u }$

Quizplus · Accepted Answer

The expression $\tan \left( \operatorname { arcsec } \frac { \sqrt { \mathrm { u } ^ { 2 } + 25 } } { \mathrm { u } } \right)$ simplifies to $\frac{5}{u}$ by recognizing that arcsec is the inverse of the secant function, which gives the ratio of the hypotenuse over the adjacent side in a right triangle. The given expression represents a triangle where the hypotenuse is $\sqrt{u^2 + 25}$ and the adjacent side is $u$, making the opposite side $5$, thus the tangent (opposite/adjacent) is $\frac{5}{u}$.

Write the Following as an Algebraic Expression in U, U tan⁡(arcsec⁡u2+25u)\tan \left( \operatorname { arcsec } \frac { \sqrt { \mathrm { u } ^ { 2 } + 25 } } { \mathrm { u } } \right)tan(arcsecuu2+25​​)

Write the Following as an Algebraic Expression in U, U $\tan \left( \operatorname { arcsec } \frac { \sqrt { \mathrm { u } ^ { 2 } + 25 } } { \mathrm { u } } \right)$