Write the trigonometric expression as an algebraic expression in u.
-$\cos \left( \tan ^ { - 1 } u \right)$
A) $u \sqrt { u ^ { 2 } + 1 }$
B) $\frac { u } { \sqrt { u ^ { 2 } + 1 } }$
C) $\frac { 1 } { \sqrt { u ^ { 2 } + 1 } }$
D) $\frac { 1 } { \sqrt { \mathrm { u } ^ { 2 } - 1 } }$

Question

Write the trigonometric expression as an algebraic expression in u.
-$\cos \left( \tan ^ { - 1 } u \right)$ 
A) $u \sqrt { u ^ { 2 } + 1 }$
B) $\frac { u } { \sqrt { u ^ { 2 } + 1 } }$
C) $\frac { 1 } { \sqrt { u ^ { 2 } + 1 } }$
D) $\frac { 1 } { \sqrt { \mathrm { u } ^ { 2 } - 1 } }$

Quizplus · Accepted Answer

To express $\cos(\tan^{-1}(u))$ as an algebraic expression, consider a right triangle where the opposite side is $u$ and the adjacent side is $1$. The hypotenuse, using the Pythagorean theorem, is $\sqrt{u^2 + 1}$. Thus, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{1}{\sqrt{u^2 + 1}}$, where $\theta = \tan^{-1}(u)$.

Write the Trigonometric Expression as an Algebraic Expression in U cos⁡(tan⁡−1u)\cos \left( \tan ^ { - 1 } u \right)cos(tan−1u)

Write the Trigonometric Expression as an Algebraic Expression in U $\cos \left( \tan ^ { - 1 } u \right)$