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

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

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

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

- 1

Solution steps

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

Rewrite using trig identities:

tan (\frac{3 π}{4})

= tan (\frac{3 π}{4})

Rewrite using trig identities:

\frac{sin ( \frac{3 π}{4} )}{cos ( \frac{3 π}{4} )}

= \frac{sin ( \frac{3 π}{4} )}{cos ( \frac{3 π}{4} )}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

= \frac{\frac{2}{2}}{- \frac{2}{2}}

Simplify

\frac{\frac{2}{2}}{- \frac{2}{2}} : - 1

= - 1

sin (11 3^{\circ})

arctan (0.52)

arctan (0.89)

sin (2 0^{\circ}) cos (8 0^{\circ}) - cos (2 0^{\circ}) sin (8 0^{\circ})

arccot (- \frac{1}{2})

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