What is the value of (tan(60)-tan(30))/(1+tan(60)tan(30)) ?

The value of (tan(60)-tan(30))/(1+tan(60)tan(30)) is (sqrt(3))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(tan(60)-tan(30))/(1+tan(60)tan(30))

\frac{tan ( 6 0 ^{\circ} ) - tan ( 3 0 ^{\circ} )}{1 + tan ( 6 0 ^{\circ} ) tan ( 3 0 ^{\circ} )}

\frac{3}{3}

Solution steps

\frac{tan ( 6 0 ^{\circ} ) - tan ( 3 0 ^{\circ} )}{1 + tan ( 6 0 ^{\circ} ) tan ( 3 0 ^{\circ} )}

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

\frac{3 - \frac{3}{3}}{1 + 3 \frac{3}{3}} : \frac{3}{3}

= \frac{3}{3}

sin (arctan (- 8))

cot (\frac{11 π}{4})

cos (\frac{3 π}{10})

csc (- \frac{5 π}{3})

sin (\frac{15 π}{2})

What is the value of (tan(60)-tan(30))/(1+tan(60)tan(30)) ?
The value of (tan(60)-tan(30))/(1+tan(60)tan(30)) is (sqrt(3))/3