What is the value of (2tan(pi/(10)))/(1-tan^2(pi/(10))) ?

The value of (2tan(pi/(10)))/(1-tan^2(pi/(10))) is (sqrt(2)(sqrt(5)-1)sqrt(5-\sqrt{5)})/4

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(2tan(pi/(10)))/(1-tan^2(pi/(10)))

\frac{2 tan ( \frac{π}{10} )}{1 - tan ^{2} ( \frac{π}{10} )}

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

Solution steps

\frac{2 tan ( \frac{π}{10} )}{1 - tan ^{2} ( \frac{π}{10} )}

Rewrite using trig identities:

tan (\frac{π}{5})

= 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}

- sin (5)

- 4 cos (\frac{π}{4})

500 cos (6 0^{\circ})

- 4 cos (\frac{π}{2})

arcsin (\frac{13}{14})

What is the value of (2tan(pi/(10)))/(1-tan^2(pi/(10))) ?
The value of (2tan(pi/(10)))/(1-tan^2(pi/(10))) is (sqrt(2)(sqrt(5)-1)sqrt(5-\sqrt{5)})/4