What is the value of tan(arccos(1/9)) ?

The value of tan(arccos(1/9)) is 4sqrt(5)

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tan(arccos(1/9))

tan (arccos (\frac{1}{9}))

45

Decimal Notation

8.94427 \dots

Solution steps

tan (arccos (\frac{1}{9}))

Rewrite using trig identities:

tan (arccos (\frac{1}{9})) = \frac{1 - ( \frac{1}{9} ) ^{2}}{( \frac{1}{9} )}

Use the following identity:

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

= \frac{1 - ( \frac{1}{9} ) ^{2}}{( \frac{1}{9} )}

= \frac{1 - ( \frac{1}{9} ) ^{2}}{\frac{1}{9}}

Simplify

= 45

sin (4 \cdot \frac{π}{4})

\frac{sin ( 3 0 ^{\circ} )}{sin ( 22. 5 ^{\circ} )}

\frac{cos ( \frac{π}{6} )}{- sin ( \frac{π}{6} )}

cos^{2} (\frac{3 π}{8}) + cos^{2} (\frac{π}{8})

cos (\frac{3 π}{4}) + sin (\frac{3 π}{4})

What is the value of tan(arccos(1/9)) ?
The value of tan(arccos(1/9)) is 4sqrt(5)