What is tan(arccos(y/5)) ?

The solution to tan(arccos(y/5)) is (sqrt(25-y^2))/y

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simplify tan(arccos(y/5))

simplify

tan (arccos (\frac{y}{5}))

\frac{25 - y ^{2}}{y}

Solution steps

tan (arccos (\frac{y}{5}))

Use the following identity:

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

= \frac{1 - ( \frac{y}{5} ) ^{2}}{( \frac{y}{5} )}

Simplify

= \frac{25 - y ^{2}}{y}

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