What is the value of tan(arccos(1/5)) ?

The value of tan(arccos(1/5)) is 2sqrt(6)

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tan(arccos(1/5))

tan (arccos (\frac{1}{5}))

26

Decimal Notation

4.89897 \dots

Solution steps

tan (arccos (\frac{1}{5}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= 26

- arccos (0)

- 100 cos (6 0^{\circ})

arccos (\frac{16}{65})

tan (23 0^{\circ})

(sec (3 0^{\circ}) + sin (6 0^{\circ}))^{2}

What is the value of tan(arccos(1/5)) ?
The value of tan(arccos(1/5)) is 2sqrt(6)