What is the value of tan(pi/(16)) ?

The value of tan(pi/(16)) is sqrt(-4\sqrt{2+\sqrt{2)}-2sqrt(2)sqrt(2+\sqrt{2)}+7+4sqrt(2)}

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tan(pi/(16))

tan (\frac{π}{16})

- 4 2 + 2 - 22 2 + 2 + 7 + 42

Solution steps

tan (\frac{π}{16})

Rewrite using trig identities:

\frac{1 - cos ( \frac{π}{8} )}{1 + cos ( \frac{π}{8} )}

= \frac{1 - cos ( \frac{π}{8} )}{1 + cos ( \frac{π}{8} )}

Rewrite using trig identities:

cos (\frac{π}{8}) = \frac{2 + 2}{2}

= \frac{1 - \frac{2 + 2}{2}}{1 + \frac{2 + 2}{2}}

Simplify

\frac{1 - \frac{2 + 2}{2}}{1 + \frac{2 + 2}{2}} : - 4 2 + 2 - 22 2 + 2 + 7 + 42

= - 4 2 + 2 - 22 2 + 2 + 7 + 42

cos (- \frac{9 π}{4})

arccos (cos (\frac{π}{2}))

sec (\frac{π}{8})

cos (\frac{19 π}{3})

tan (arcsin (\frac{2}{5}))

What is the value of tan(pi/(16)) ?
The value of tan(pi/(16)) is sqrt(-4\sqrt{2+\sqrt{2)}-2sqrt(2)sqrt(2+\sqrt{2)}+7+4sqrt(2)}