Factor the trigonometric expression and simplify.
-$\tan \frac { \pi } { 12 }$
A) $- 2 - \sqrt { 3 }$
B) $- 2 + \sqrt { 3 }$
C) $2 - \sqrt { 3 }$
D) $2 + \sqrt { 3 }$

Question

Quizplus · Accepted Answer

The expression $\tan \frac{\pi}{12}$ can be simplified using the half-angle formula for tangent, where $\tan \frac{\theta}{2} = \sqrt{\frac{1 - \cos \theta}{1 + \cos \theta}}$. For $\frac{\pi}{12}$, we can use $\theta = \frac{\pi}{6}$ to find $\tan \frac{\pi}{12} = \sqrt{\frac{1 - \cos \frac{\pi}{6}}{1 + \cos \frac{\pi}{6}}}$. Knowing $\cos \frac{\pi}{6} = \sqrt{3}/2$, we simplify to get $2 - \sqrt{3}$.

Factor the Trigonometric Expression and Simplify tan⁡π12\tan \frac { \pi } { 12 }tan12π​

Factor the Trigonometric Expression and Simplify $\tan \frac { \pi } { 12 }$