What is the value of (2tan(60))/(1-tan^2(60)) ?

The value of (2tan(60))/(1-tan^2(60)) is -sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(2tan(60))/(1-tan^2(60))

\frac{2 tan ( 6 0 ^{\circ} )}{1 - tan ^{2} ( 6 0 ^{\circ} )}

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

\frac{2 tan ( 6 0 ^{\circ} )}{1 - tan ^{2} ( 6 0 ^{\circ} )}

Use the following trivial identity:

tan (6 0^{\circ}) = 3

tan (6 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}

= 3

= \frac{2 3}{1 - ( 3 ) ^{2}}

Simplify

\frac{2 3}{1 - ( 3 ) ^{2}} : - 3

\frac{2 3}{1 - ( 3 ) ^{2}}

(3)^{2} = 3

(3)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 3

= \frac{2 3}{1 - 3}

Subtract the numbers:

1 - 3 = - 2

= \frac{2 3}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 3}{2}

Divide the numbers:

\frac{2}{2} = 1

= - 3

= - 3

cot (\frac{1}{3})

sec (\frac{- 5 π}{4})

cos (68. 2^{\circ})

cos (- 4 0^{\circ})

tan (2 arcsin (\frac{5}{13}))

What is the value of (2tan(60))/(1-tan^2(60)) ?
The value of (2tan(60))/(1-tan^2(60)) is -sqrt(3)