Find the exact value of the expression.
-$\tan \frac { 5 \pi } { 12 }$
A) $2 + \sqrt { 3 }$
B) $2 - \sqrt { 3 }$
C) $\sqrt { 3 } - 2$
D) $- 2 - \sqrt { 3 }$

Question

Quizplus · Accepted Answer

The exact value of $\tan \frac { 5 \pi } { 12 }$ can be found by expressing $\frac { 5 \pi } { 12 }$ as the sum of two angles whose tangent values are known. Specifically, $\frac { 5 \pi } { 12 } = \frac { 4 \pi } { 12 } + \frac { \pi } { 12 } = \frac { \pi } { 3 } + \frac { \pi } { 4 }$. Using the tangent sum formula, $\tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}$, with $\tan \frac { \pi } { 3 } = \sqrt { 3 }$ and $\tan \frac { \pi } { 4 } = 1$, we get $\tan \frac { 5 \pi } { 12 } = \frac{\sqrt { 3 } + 1}{1 - \sqrt { 3 }} = 2 - \sqrt { 3 }$.

Find the Exact Value of the Expression tan⁡5π12\tan \frac { 5 \pi } { 12 }tan125π​

Find the Exact Value of the Expression $\tan \frac { 5 \pi } { 12 }$