What is the value of tan((13pi)/(12)) ?

The value of tan((13pi)/(12)) is 2-sqrt(3)

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tan((13pi)/(12))

tan (\frac{13 π}{12})

2 - 3

Solution steps

tan (\frac{13 π}{12})

tan (\frac{13 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

arctan (- 3)

cos (67. 5^{\circ})

cos^{2} (1)

sin (3 6^{\circ})

arctan (\frac{5}{3})

What is the value of tan((13pi)/(12)) ?
The value of tan((13pi)/(12)) is 2-sqrt(3)