Find the expression as the tangent of an angle. $\frac { \tan 130 ^ { \circ } - \tan 30 ^ { \circ } } { 1 + \tan 130 ^ { \circ } \tan 30 ^ { \circ } }$
A) $\tan ^ { - 1 } 100 ^ { \circ }$
B) $\tan ^ { - 1 } 130 ^ { \circ }$
C) $\tan 160 ^ { \circ }$
D) $\tan 100 ^ { \circ }$
E) $\tan 30 ^ { \circ }$

Question

Find the expression as the tangent of an angle.   $\frac { \tan 130 ^ { \circ } - \tan 30 ^ { \circ } } { 1 + \tan 130 ^ { \circ } \tan 30 ^ { \circ } }$  
A) $\tan ^ { - 1 } 100 ^ { \circ }$
B) $\tan ^ { - 1 } 130 ^ { \circ }$
C) $\tan 160 ^ { \circ }$
D) $\tan 100 ^ { \circ }$
E) $\tan 30 ^ { \circ }$

Quizplus · Accepted Answer

This expression can be simplified using the tangent addition formula: $\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$. Substituting $A = 130^\circ$ and $B = 30^\circ$, we get $\tan(130^\circ - 30^\circ) = \tan 100^\circ$.

Find the Expression as the Tangent of an Angle tan⁡130∘−tan⁡30∘1+tan⁡130∘tan⁡30∘\frac { \tan 130 ^ { \circ } - \tan 30 ^ { \circ } } { 1 + \tan 130 ^ { \circ } \tan 30 ^ { \circ } }1+tan130∘tan30∘tan130∘−tan30∘​

Find the Expression as the Tangent of an Angle $\frac { \tan 130 ^ { \circ } - \tan 30 ^ { \circ } } { 1 + \tan 130 ^ { \circ } \tan 30 ^ { \circ } }$