Factor the trigonometric expression and simplify.
-$\tan \left( x - \frac { \pi } { 3 } \right)$
A) $\frac { \tan x - \sqrt { 3 } } { 1 + \sqrt { 3 } \tan x }$
B) $\frac { 1 + \sqrt { 3 } \tan x } { \sqrt { 3 } - \tan x }$
C) $- \tan x$
D) $\tan x$

Question

Quizplus · Accepted Answer

The correct factorization and simplification of $\tan \left( x - \frac { \pi } { 3 } \right)$ is achieved using the tangent subtraction formula: $\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$. Applying this formula with $A = x$ and $B = \frac{\pi}{3}$, where $\tan\left(\frac{\pi}{3}\right) = \sqrt{3}$, we get $\frac { \tan x - \sqrt { 3 } } { 1 + \sqrt { 3 } \tan x }$.

Factor the Trigonometric Expression and Simplify tan⁡(x−π3)\tan \left( x - \frac { \pi } { 3 } \right)tan(x−3π​)

Factor the Trigonometric Expression and Simplify $\tan \left( x - \frac { \pi } { 3 } \right)$