Write the expression as an algebraic (nontrigonometric) expression in $u, u > 0$ .
$\tan (\arccos u)$
$\tan (\arccos u) =$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Answer

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Answer

$\tan (\arccos u) = \frac{\sqrt{1 - u^{2}}}{u}$

Steps

Step 1 ：Given the trigonometric expression $\tan (\arccos u)$ , we are asked to express it in terms of $u$ only.

Step 2 ：We can use the identity $\tan (θ) = \frac{\sin (θ)}{\cos (θ)}$ .

Step 3 ：Since $\cos (\arccos u) = u$ , we can substitute $θ$ with $\arccos u$ in the above equation.

Step 4 ：We also know that $\sin (θ) = \sqrt{1 - \cos^{2} (θ)}$ . So, substituting $θ$ with $\arccos u$ gives us $\sin (\arccos u) = \sqrt{1 - u^{2}}$ .

Step 5 ：Substituting these values into the identity for $\tan (θ)$ gives us the expression in terms of $u$ only.

Step 6 ： $\tan (\arccos u) = \frac{\sqrt{1 - u^{2}}}{u}$

Step 7 ： $\tan (\arccos u) = \frac{\sqrt{1 - u^{2}}}{u}$

Write the expression as an algebraic (nontrigonometric) expression in u,u>0.tan⁡(arccos⁡u)tan⁡(arccos⁡u)=(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Answer

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Write the expression as an algebraic (nontrigonometric) expression in $u, u > 0$ .
$\tan (\arccos u)$
$\tan (\arccos u) =$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)