What is the value of (2tan((7pi)/8))/(1-2tan^2((7pi)/8)) ?

The value of (2tan((7pi)/8))/(1-2tan^2((7pi)/8)) is -(6+2sqrt(2))/7

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(2tan((7pi)/8))/(1-2tan^2((7pi)/8))

\frac{2 tan ( \frac{7 π}{8} )}{1 - 2 tan ^{2} ( \frac{7 π}{8} )}

- \frac{6 + 2 2}{7}

Solution steps

\frac{2 tan ( \frac{7 π}{8} )}{1 - 2 tan ^{2} ( \frac{7 π}{8} )}

Rewrite using trig identities:

tan (\frac{7 π}{8}) = - 3 - 22

= \frac{2 ( - 3 - 2 2 )}{1 - 2 ( - 3 - 2 2 ) ^{2}}

Simplify

\frac{2 ( - 3 - 2 2 )}{1 - 2 ( - 3 - 2 2 ) ^{2}} : - \frac{6 + 2 2}{7}

= - \frac{6 + 2 2}{7}

arccos (\frac{2}{7})

arccos (\frac{5}{5 10})

10 \cdot tan (2 5^{\circ})

sin (0.7 π)

sin (\frac{\frac{π}{2}}{3})

What is the value of (2tan((7pi)/8))/(1-2tan^2((7pi)/8)) ?
The value of (2tan((7pi)/8))/(1-2tan^2((7pi)/8)) is -(6+2sqrt(2))/7