What is tan(arccos(3v)) ?

The solution to tan(arccos(3v)) is (sqrt(1-9v^2))/(3v)

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simplify tan(arccos(3v))

simplify

tan (arccos (3 v))

\frac{1 - 9 v ^{2}}{3 v}

Solution steps

tan (arccos (3 v))

Use the following identity:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( 3 v ) ^{2}}{3 v}

1 - (3 v)^{2} = 1 - 9 v^{2}

= \frac{1 - 9 v ^{2}}{3 v}

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What is tan(arccos(3v)) ?
The solution to tan(arccos(3v)) is (sqrt(1-9v^2))/(3v)