Find the expression as the tangent of an angle. $$\frac { \tan 60 ^ { \circ } - \tan 20 ^ { \circ } } { 1 + \tan 60 ^ { \circ } \tan 20 ^ { \circ } }$$
A) $\tan 40 ^ { \circ }$
B) $\tan 60 ^ { \circ }$
C) $\tan ^ { - 1 } 80 ^ { \circ }$
D) $\tan 20 ^ { \circ }$
E) $\tan ^ { - 1 } 40 ^ { \circ }$

Question

Find the expression as the tangent of an angle.​ $$\frac { \tan 60 ^ { \circ } - \tan 20 ^ { \circ } } { 1 + \tan 60 ^ { \circ } \tan 20 ^ { \circ } }$$ ​
A) $\tan 40 ^ { \circ }$
B) $\tan 60 ^ { \circ }$
C) $\tan ^ { - 1 } 80 ^ { \circ }$
D) $\tan 20 ^ { \circ }$
E) $\tan ^ { - 1 } 40 ^ { \circ }$

Quizplus · Accepted Answer

This expression can be simplified using the tangent subtraction formula, $\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$, which directly matches the given expression with $A = 60^\circ$ and $B = 20^\circ$, resulting in $\tan(60^\circ - 20^\circ) = \tan 40^\circ$.

Find the Expression as the Tangent of an Angle tan⁡60∘−tan⁡20∘1+tan⁡60∘tan⁡20∘\frac { \tan 60 ^ { \circ } - \tan 20 ^ { \circ } } { 1 + \tan 60 ^ { \circ } \tan 20 ^ { \circ } }1+tan60∘tan20∘tan60∘−tan20∘​

Find the Expression as the Tangent of an Angle $\frac { \tan 60 ^ { \circ } - \tan 20 ^ { \circ } } { 1 + \tan 60 ^ { \circ } \tan 20 ^ { \circ } }$