What is the value of tan((4pi)/5) ?

The value of tan((4pi)/5) is -(sqrt(2)(sqrt(5)-1)sqrt(5-\sqrt{5)})/4

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tan((4pi)/5)

tan (\frac{4 π}{5})

- \frac{2 ( 5 - 1 ) 5 - 5}{4}

Solution steps

tan (\frac{4 π}{5})

Rewrite using trig identities:

\frac{sin ( \frac{4 π}{5} )}{cos ( \frac{4 π}{5} )}

= \frac{sin ( \frac{4 π}{5} )}{cos ( \frac{4 π}{5} )}

Rewrite using trig identities:

sin (\frac{4 π}{5}) = \frac{2 5 - 5}{4}

Rewrite using trig identities:

cos (\frac{4 π}{5}) = - \frac{5 + 1}{4}

= \frac{\frac{2 5 - 5}{4}}{- \frac{5 + 1}{4}}

Simplify

\frac{\frac{2 5 - 5}{4}}{- \frac{5 + 1}{4}} : - \frac{2 ( 5 - 1 ) 5 - 5}{4}

= - \frac{2 ( 5 - 1 ) 5 - 5}{4}

4 sin (- \frac{π}{2})

tan (90 0^{\circ})

arcsin (\frac{4}{10})

tan^{2} (4 5^{\circ} - 1 5^{\circ})

arctan (\frac{3}{- 2})

What is the value of tan((4pi)/5) ?
The value of tan((4pi)/5) is -(sqrt(2)(sqrt(5)-1)sqrt(5-\sqrt{5)})/4