What is tan(arccos(x/2)) ?

The solution to tan(arccos(x/2)) is (sqrt(4-x^2))/x

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simplify tan(arccos(x/2))

simplify

tan (arccos (\frac{x}{2}))

\frac{4 - x ^{2}}{x}

Solution steps

tan (arccos (\frac{x}{2}))

Use the following identity:

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

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

Simplify

= \frac{4 - x ^{2}}{x}

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