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

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

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simplify tan(arccos(x/5))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

1 + (tan (x))^{2}

sin (- x) + sin (x)

cos (72 0^{\circ} + x)

cot (\frac{π}{2} - x) cos (x)

cos (2 (x + \frac{π}{2}))