What is the value of tan((11pi)/6+pi/4) ?

The value of tan((11pi)/6+pi/4) is 2-sqrt(3)

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tan((11pi)/6+pi/4)

tan (\frac{11 π}{6} + \frac{π}{4})

2 - 3

Solution steps

tan (\frac{11 π}{6} + \frac{π}{4})

Simplify:

\frac{11 π}{6} + \frac{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

sin (- \frac{5}{13})

cos (\frac{8}{5})

80 cos (4 0^{\circ})

arccos (\frac{2}{8})

csc (- \frac{2}{3} π)

What is the value of tan((11pi)/6+pi/4) ?
The value of tan((11pi)/6+pi/4) is 2-sqrt(3)