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

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

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tan(pi/5)

tan (\frac{π}{5})

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

Solution steps

tan (\frac{π}{5})

Rewrite using trig identities:

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

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

Rewrite using trig identities:

sin (\frac{π}{5}) = \frac{2 5 - 5}{4}

Rewrite using trig identities:

cos (\frac{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}

cos (2 (0))

sec (\frac{11 π}{3})

sec (- 9 0^{\circ})

cos (3 9^{\circ})

cot (\frac{23 π}{4})

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