What is tan(arccos(y/8)) ?

The solution to tan(arccos(y/8)) is (sqrt(64-y^2))/y

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simplify tan(arccos(y/8))

simplify

tan (arccos (\frac{y}{8}))

\frac{64 - y ^{2}}{y}

Solution steps

tan (arccos (\frac{y}{8}))

Use the following identity:

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

= \frac{1 - ( \frac{y}{8} ) ^{2}}{( \frac{y}{8} )}

Simplify

= \frac{64 - y ^{2}}{y}

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