Use an identity to write the expression as a single trigonometric function or as a single number.
-$\frac { 2 \tan 30 ^ { \circ } } { 1 - \tan ^ { 2 } 30 ^ { \circ } }$
A) $\sqrt { 3 }$
B) $\frac { \sqrt { 2 } } { 2 }$
C) $\frac { \sqrt { 2 } } { 4 }$
D) $\frac { \sqrt { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

This expression is an application of the tangent double-angle identity, $\tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)}$. Substituting $\theta = 30^\circ$, where $\tan(30^\circ) = \frac{\sqrt{3}}{3}$, into the identity gives $\tan(60^\circ) = \sqrt{3}$.

Use an Identity to Write the Expression as a Single 2tan⁡30∘1−tan⁡230∘\frac { 2 \tan 30 ^ { \circ } } { 1 - \tan ^ { 2 } 30 ^ { \circ } }1−tan230∘2tan30∘​

Use an Identity to Write the Expression as a Single $\frac { 2 \tan 30 ^ { \circ } } { 1 - \tan ^ { 2 } 30 ^ { \circ } }$