Write the given expression as the tangent of an angle. $\frac { \tan 3 x + \tan 4 x } { 1 - \tan 3 x \tan 4 x }$
A) $\tan ( 7 x )$
B) $\tan ( 3 x )$
C) $\tan ( 5 x )$
D) $\tan ( - x )$
E) $\tan ( - 5 x )$

Question

Quizplus · Accepted Answer

The given expression is in the form of the tangent addition formula, $\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$, where $A = 3x$ and $B = 4x$. Therefore, it simplifies to $\tan(3x + 4x) = \tan(7x)$.

Write the Given Expression as the Tangent of an Angle tan⁡3x+tan⁡4x1−tan⁡3xtan⁡4x\frac { \tan 3 x + \tan 4 x } { 1 - \tan 3 x \tan 4 x }1−tan3xtan4xtan3x+tan4x​

Write the Given Expression as the Tangent of an Angle $\frac { \tan 3 x + \tan 4 x } { 1 - \tan 3 x \tan 4 x }$