Find the expression as the tangent of an angle. $\frac { \tan 3 x + \tan x } { 1 - \tan 3 x \tan x }$
A) $\tan 2 x$
B) $\tan 3 x$
C) $\tan 4 x$
D) $\tan ^ { - 1 } 4 x$
E) $\tan ^ { - 1 } 2 x$

Question

Find the expression as the tangent of an angle.   $\frac { \tan 3 x + \tan x } { 1 - \tan 3 x \tan x }$  
A) $\tan 2 x$
B) $\tan 3 x$
C) $\tan 4 x$
D) $\tan ^ { - 1 } 4 x$
E) $\tan ^ { - 1 } 2 x$

Quizplus · Accepted Answer

This expression can be simplified using the tangent addition formula, $\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$. By comparing the given expression $\frac{\tan 3x + \tan x}{1 - \tan 3x \tan x}$ with the formula, it's clear that it represents $\tan(3x + x) = \tan 4x$, making option C the correct answer.

Find the Expression as the Tangent of an Angle tan⁡3x+tan⁡x1−tan⁡3xtan⁡x\frac { \tan 3 x + \tan x } { 1 - \tan 3 x \tan x }1−tan3xtanxtan3x+tanx​

Find the Expression as the Tangent of an Angle $\frac { \tan 3 x + \tan x } { 1 - \tan 3 x \tan x }$