Use Sum and Difference Formulas for Tangents
Find the exact value by using a difference identity.
-$\tan \frac { 13 \pi } { 12 }$
A) $2 - \sqrt { 3 }$
B) $2 + \sqrt { 3 }$
C) $\sqrt { 3 } - 2$
D) $- 2 - \sqrt { 3 }$

Question

Quizplus · Accepted Answer

The exact value of $\tan \frac { 13 \pi } { 12 }$ can be found by using the difference identity for tangent: $\tan (A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$. Here, we can express $\frac { 13 \pi } { 12 }$ as $\pi - \frac{\pi}{4}$ or $\frac{\pi}{3} - \frac{\pi}{4}$, which simplifies to $\tan(\frac{\pi}{3} - \frac{\pi}{4})$. Using the tangent values for $\frac{\pi}{3}$ and $\frac{\pi}{4}$, which are $\sqrt{3}$ and $1$ respectively, we get $\frac{\sqrt{3} - 1}{1 + \sqrt{3}}$, which simplifies to $2 - \sqrt{3}$.

Use Sum and Difference Formulas for Tangents Find the Exact tan⁡13π12\tan \frac { 13 \pi } { 12 }tan1213π​

Use Sum and Difference Formulas for Tangents
Find the Exact $\tan \frac { 13 \pi } { 12 }$