What is the value of (2tan(15))/(1-tan^2(15)) ?

The value of (2tan(15))/(1-tan^2(15)) is (sqrt(3))/3

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(2tan(15))/(1-tan^2(15))

\frac{2 tan ( 1 5 ^{\circ} )}{1 - tan ^{2} ( 1 5 ^{\circ} )}

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

\frac{2 tan ( 1 5 ^{\circ} )}{1 - tan ^{2} ( 1 5 ^{\circ} )}

Rewrite using trig identities:

tan (3 0^{\circ})

\frac{2 tan ( 1 5 ^{\circ} )}{1 - tan ^{2} ( 1 5 ^{\circ} )}

Use the Double Angle identity:

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

= tan (2 \cdot 1 5^{\circ})

Simplify

= tan (3 0^{\circ})

= tan (3 0^{\circ})

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{3}{3}

cos (1 π)

2 sin (\frac{5 π}{4})

arccos (\frac{1}{5})

tan (arctan (1))

cos (4 1^{\circ})

What is the value of (2tan(15))/(1-tan^2(15)) ?
The value of (2tan(15))/(1-tan^2(15)) is (sqrt(3))/3