Write the expression as the sine, cosine, or tangent of an angle.
-$\frac { \tan ( \pi / 5 ) + \tan ( \pi / 3 ) } { 1 - \tan ( \pi / 5 ) \tan ( \pi / 3 ) }$
A) $\tan \left( \frac { 2 \pi } { 15 } \right)$
B) $\tan \left( \frac { \pi } { 15 } \right)$
C) $\tan \left( \frac { \pi } { 8 } \right)$
D) $\tan \left( \frac { 8 \pi } { 15 } \right)$

Question

Quizplus · Accepted Answer

The expression is a form of the tangent addition formula, $\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$, where $A = \pi/5$ and $B = \pi/3$. Adding these angles gives $\pi/5 + \pi/3 = 8\pi/15$, so the expression simplifies to $\tan(8\pi/15)$.

Write the Expression as the Sine, Cosine, or Tangent of an Angle