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) $- 2$
B) $- \sqrt { 3 }$
C) $- \frac { 1 } { 2 }$
D) $- \frac { \sqrt { 3 } } { 3 }$

Question

Quizplus · Accepted Answer

The expression is in the form of the tangent difference identity, $\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$. Here, $A = 100^\circ$ and $B = -20^\circ$, so the expression simplifies to $\tan(100^\circ - (-20^\circ)) = \tan(120^\circ)$. The exact value of $\tan(120^\circ)$ is $-\sqrt{3}$, which corresponds to choice B.

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 $\frac { \tan 100 ^ { \circ } - \tan ( - 20 ) ^ { \circ } } { 1 + \tan 100 ^ { \circ } \tan ( - 20 ) ^ { \circ } }$