Find an algebraic expression equivalent to the given expression.
-$\cos ( \operatorname { arccot } u )$
A) $\sqrt { u ^ { 2 } - 1 }$
B) $\frac { \sqrt { \mathrm { u } ^ { 2 } - 1 } } { \mathrm { u } }$
C) $\sqrt { \mathrm { u } ^ { 2 } + 1 }$
D) $\frac { u \sqrt { \mathrm { u } ^ { 2 } + 1 } } { \mathrm { u } ^ { 2 } + 1 }$

Question

Quizplus · Accepted Answer

The expression $\cos(\operatorname{arccot} u)$ can be derived using the identity $\cos(\theta) = \frac{1}{\sqrt{1 + \cot^2(\theta)}}$. Since $\theta = \operatorname{arccot}(u)$, $\cot(\theta) = u$, and $\cos(\theta) = \frac{1}{\sqrt{1 + u^2}}$. Simplifying $\frac{u}{\sqrt{u^2 + 1}}$ gives the equivalent expression.

Find an Algebraic Expression Equivalent to the Given Expression cos⁡(arccot⁡u)\cos ( \operatorname { arccot } u )cos(arccotu)

Find an Algebraic Expression Equivalent to the Given Expression $\cos ( \operatorname { arccot } u )$