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

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

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

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

1

Solution steps

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

Rewrite using trig identities:

tan (\frac{π}{4})

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

Use the Double Angle identity:

\frac{2 tan ( x )}{1 - tan ^{2} ( x )} = tan (2 x)

= tan (2 \cdot \frac{π}{8})

Simplify:

2 \cdot \frac{π}{8} = \frac{π}{4}

2 \cdot \frac{π}{8}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{8}

Cancel the common factor:

2

= \frac{π}{4}

= tan (\frac{π}{4})

= tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 1

cos (13 2^{\circ})

1 - 2 sin^{2} (\frac{1}{8})

cos (\frac{5 π}{24})

250 cos (6 0^{\circ})

cos (\frac{17}{12} π)

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