What is the value of (2tan((3pi)/8))/(1-tan^2((3pi)/8)) ?

The value of (2tan((3pi)/8))/(1-tan^2((3pi)/8)) is -1

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(2tan((3pi)/8))/(1-tan^2((3pi)/8))

\frac{2 tan ( \frac{3 π}{8} )}{1 - tan ^{2} ( \frac{3 π}{8} )}

- 1

Solution steps

\frac{2 tan ( \frac{3 π}{8} )}{1 - tan ^{2} ( \frac{3 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

arcsin (\frac{1}{1})

cos (\frac{13 π}{8})

arccos (- 0.88)

tan (- \frac{3}{4})

\frac{7}{tan ( 6 5 ^{\circ} )}

What is the value of (2tan((3pi)/8))/(1-tan^2((3pi)/8)) ?
The value of (2tan((3pi)/8))/(1-tan^2((3pi)/8)) is -1