What is the value of tan((7pi)/(12)) ?

The value of tan((7pi)/(12)) is -2-sqrt(3)

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tan((7pi)/(12))

tan (\frac{7 π}{12})

- 2 - 3

Solution steps

tan (\frac{7 π}{12})

Rewrite using trig identities:

\frac{tan ( \frac{π}{3} ) + tan ( \frac{π}{4} )}{1 - tan ( \frac{π}{3} ) tan ( \frac{π}{4} )}

= \frac{tan ( \frac{π}{3} ) + tan ( \frac{π}{4} )}{1 - tan ( \frac{π}{3} ) tan ( \frac{π}{4} )}

Use the following trivial identity:

tan (\frac{π}{3}) = 3

Use the following trivial identity:

tan (\frac{π}{4}) = 1

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

Simplify

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

= - 2 - 3

cos (\frac{π}{4})

tan (- \frac{π}{12})

arccos (- \frac{2}{2})

sec^{2} (π)

sin (3 x) = \frac{2}{2}

What is the value of tan((7pi)/(12)) ?
The value of tan((7pi)/(12)) is -2-sqrt(3)