What is the value of tan((5pi)/6+(5pi)/4) ?

The value of tan((5pi)/6+(5pi)/4) is 2-sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan((5pi)/6+(5pi)/4)

tan (\frac{5 π}{6} + \frac{5 π}{4})

2 - 3

Solution steps

tan (\frac{5 π}{6} + \frac{5 π}{4})

Simplify:

\frac{5 π}{6} + \frac{5 π}{4} = \frac{25 π}{12}

= tan (\frac{25 π}{12})

tan (\frac{25 π}{12}) = tan (\frac{π}{12})

= tan (\frac{π}{12})

Rewrite using trig identities:

\frac{tan ( \frac{π}{4} ) - tan ( \frac{π}{6} )}{1 + tan ( \frac{π}{4} ) tan ( \frac{π}{6} )}

= \frac{tan ( \frac{π}{4} ) - tan ( \frac{π}{6} )}{1 + tan ( \frac{π}{4} ) tan ( \frac{π}{6} )}

Use the following trivial identity:

tan (\frac{π}{4}) = 1

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

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

Simplify

\frac{1 - \frac{3}{3}}{1 + 1 \cdot \frac{3}{3}} : 2 - 3

= 2 - 3

cos (12 0^{\circ} - 4 5^{\circ})

arccos (0.866)

\frac{sin ( π ) + π cos ( π )}{cos ( π ) - π sin ( π )}

cos (21 5^{\circ})

cos (π^{3})

What is the value of tan((5pi)/6+(5pi)/4) ?
The value of tan((5pi)/6+(5pi)/4) is 2-sqrt(3)