Use a sum or difference identity to find the exact value.
-$\tan \frac { \pi } { 12 }$
A) $- 2 - \sqrt { 3 }$
B) $2 - \sqrt { 3 }$
C) $- 2 + \sqrt { 3 }$
D) $2 + \sqrt { 3 }$

Question

Quizplus · Accepted Answer

To find the exact value of $\tan \frac{\pi}{12}$, we can use the sum or difference formula for tangent. $\frac{\pi}{12}$ can be expressed as $\frac{\pi}{3} - \frac{\pi}{4}$. Using the difference identity for tangent, $\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$, where $A = \frac{\pi}{3}$ and $B = \frac{\pi}{4}$, we get $\tan \frac{\pi}{12} = \frac{\sqrt{3} - 1}{1 + \sqrt{3}}$, which simplifies to $2 - \sqrt{3}$.

Use a Sum or Difference Identity to Find the Exact tan⁡π12\tan \frac { \pi } { 12 }tan12π​

Use a Sum or Difference Identity to Find the Exact $\tan \frac { \pi } { 12 }$