Use a sum or difference identity to find the exact value.
-$$\frac { \tan 100 ^ { \circ } - \tan ( - 20 ) ^ { \circ } } { 1 + \tan 100 ^ { \circ } \tan ( - 20 ) ^ { \circ } }$$
A) $- \frac { \sqrt { 3 } } { 3 }$
B) $- \frac { 1 } { 2 }$
C) $- 2$
D) $- \sqrt { 3 }$

Question

Quizplus · Accepted Answer

The expression is the tangent of the sum of angles: $\tan(100^\circ + 20^\circ) = \tan(120^\circ)$, which equals $-\sqrt{3}$.

Use a Sum or Difference Identity to Find the Exact tan⁡100∘−tan⁡(−20)∘1+tan⁡100∘tan⁡(−20)∘\frac { \tan 100 ^ { \circ } - \tan ( - 20 ) ^ { \circ } } { 1 + \tan 100 ^ { \circ } \tan ( - 20 ) ^ { \circ } }1+tan100∘tan(−20)∘tan100∘−tan(−20)∘​

Use a Sum or Difference Identity to Find the Exact $\frac { \tan 100 ^ { \circ } - \tan ( - 20 ) ^ { \circ } } { 1 + \tan 100 ^ { \circ } \tan ( - 20 ) ^ { \circ } }$