Write the given expression as the tangent of an angle.
$\frac { \tan 7 x + \tan 4 x } { 1 - \tan 7 x \tan 4 x }$
A) $\tan ( - 17 x )$
B) $\tan ( 11 x )$
C) $\tan ( 7 x )$
D) $\tan ( 3 x )$
E) $\tan ( 5 x )$

Question

Write the given expression as the tangent of an angle.
 $\frac { \tan 7 x + \tan 4 x } { 1 - \tan 7 x \tan 4 x }$
A) $\tan ( - 17 x )$
B) $\tan ( 11 x )$
C) $\tan ( 7 x )$
D) $\tan ( 3 x )$
E) $\tan ( 5 x )$

Quizplus · Accepted Answer

This expression can be simplified using the tangent addition formula, $\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$. Here, $A = 7x$ and $B = 4x$, so the expression simplifies to $\tan(7x + 4x) = \tan(11x)$.

Write the Given Expression as the Tangent of an Angle tan⁡7x+tan⁡4x1−tan⁡7xtan⁡4x\frac { \tan 7 x + \tan 4 x } { 1 - \tan 7 x \tan 4 x }1−tan7xtan4xtan7x+tan4x​

Write the Given Expression as the Tangent of an Angle $\frac { \tan 7 x + \tan 4 x } { 1 - \tan 7 x \tan 4 x }$