Questions: Write the trigonometric expression as an algebraic expression in (u). [ cot left(tan ^-1 uright) ] (cot left(tan ^-1 uright)=) (Type an exact answer, using radicals as needed.)

Write the trigonometric expression as an algebraic expression in (u).
[
cot left(tan ^-1 uright)
]
(cot left(tan ^-1 uright)=) (Type an exact answer, using radicals as needed.)

Transcript text: Write the trigonometric expression as an algebraic expression in $u$. \[ \cot \left(\tan ^{-1} \mathrm{u}\right) \] $\cot \left(\tan ^{-1} \mathrm{u}\right)=$ $\square$ (Type an exact answer, using radicals as needed.)

Solution

Solution Steps

Step 1: Identify the Trigonometric Identity

Using the Pythagorean identity for $\tan$ and $\cot$.

Step 2: Express the Trigonometric Function in Terms of $u$

Given that $x = atan^-1(u)$, we express $\cot(x)$ in terms of $u$.

Step 3: Solve for the Desired Trigonometric Function

By algebraic manipulation, we find that $\cot(atan^-1(u)) = 1/u$.

Step 4: Consider the Domain and Range

Ensure the solution is within the domain and range of the original and inverse trigonometric functions.

Final Answer: $\cot(atan^-1(u)) = 1/u$

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Questions: Write the trigonometric expression as an algebraic expression in (u). [ cot left(tan ^-1 uright) ] (cot left(tan ^-1 uright)=) (Type an exact answer, using radicals as needed.)

Solution

Solution Steps

Final Answer: \(\cot(atan^-1(u)) = 1/u\)

Questions asked by other users