Find an exact value.
-$$\tan \frac { 13 \pi } { 12 }$$
A) $\frac { 2 + \sqrt { 3 } } { 4 }$
B) $\frac { 2 - \sqrt { 3 } } { 4 }$
C) $2 + \sqrt { 3 }$
D) $2 - \sqrt { 3 }$

Question

Quizplus · Accepted Answer

To find $\tan \frac{13\pi}{12}$, we use the identity $\tan(a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}$. Here, $\frac{13\pi}{12} = \pi + \frac{\pi}{12}$. Since $\tan(\pi + x) = \tan x$, we have $\tan \frac{13\pi}{12} = \tan \frac{\pi}{12}$. Using the identity $\tan \frac{\pi}{12} = 2 - \sqrt{3}$, the correct answer is D.

Find an Exact Value tan⁡13π12\tan \frac { 13 \pi } { 12 }tan1213π​

Find an Exact Value $\tan \frac { 13 \pi } { 12 }$