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

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

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(tan(15)+tan(15))/(1-tan(15)tan(15))

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

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

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

Simplify

= \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}

arctan (\frac{- 2 3}{2})

cos (\frac{4}{7})

cos^{2} (31 5^{\circ})

sin (\frac{- 13 π}{12})

sin (\frac{3 π}{7})

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