What is tan(arccos(x/3)) ?

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

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simplify tan(arccos(x/3))

simplify

tan (arccos (\frac{x}{3}))

\frac{9 - x ^{2}}{x}

Solution steps

tan (arccos (\frac{x}{3}))

Use the following identity:

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

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

Simplify

= \frac{9 - x ^{2}}{x}

tan (arcsin (\frac{x}{5}))

cos (π - nπ)

4 - 4 sin^{2} (x)

cos (arcsin (\frac{x}{5}))

sin (θ + 2 π)