What is the value of tan(arccos(15/17)) ?

The value of tan(arccos(15/17)) is 8/15

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tan(arccos(15/17))

tan (arccos (\frac{15}{17}))

\frac{8}{15}

Decimal Notation

0.53333 \dots

Solution steps

tan (arccos (\frac{15}{17}))

Rewrite using trig identities:

tan (arccos (\frac{15}{17})) = \frac{1 - ( \frac{15}{17} ) ^{2}}{( \frac{15}{17} )}

Use the following identity:

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

= \frac{1 - ( \frac{15}{17} ) ^{2}}{( \frac{15}{17} )}

= \frac{1 - ( \frac{15}{17} ) ^{2}}{\frac{15}{17}}

Simplify

= \frac{8}{15}

sin (3 0^{\circ}) + sin (4 5^{\circ})

e^{\frac{π}{4}} cos (\frac{π}{4})

\frac{sin ( 4 )}{4}

arctan (tan (- \frac{3 π}{7}))

sin (10 0^{\circ}) cos (4 0^{\circ}) - cos (10 0^{\circ}) sin (4 0^{\circ})

What is the value of tan(arccos(15/17)) ?
The value of tan(arccos(15/17)) is 8/15