Use a sum or difference identity to find the exact value.
-$$\frac { \tan 70 ^ { \circ } - \tan ( - 50 ) ^ { \circ } } { 1 + \tan 70 ^ { \circ } \tan ( - 50 ) ^ { \circ } }$$
A) $- \frac { 1 } { 2 }$
B) $- \frac { \sqrt { 3 } } { 3 }$
C) $- 2$
D) $- \sqrt { 3 }$

Question

Quizplus · Accepted Answer

The expression is a form of the tangent sum identity, $\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$. Here, $A = 70^\circ$ and $B = -50^\circ$, so $A - B = 70^\circ - (-50^\circ) = 120^\circ$. The exact value of $\tan 120^\circ$ is $-\sqrt{3}$, which corresponds to choice D.

Use a Sum or Difference Identity to Find the Exact tan⁡70∘−tan⁡(−50)∘1+tan⁡70∘tan⁡(−50)∘\frac { \tan 70 ^ { \circ } - \tan ( - 50 ) ^ { \circ } } { 1 + \tan 70 ^ { \circ } \tan ( - 50 ) ^ { \circ } }1+tan70∘tan(−50)∘tan70∘−tan(−50)∘​

Use a Sum or Difference Identity to Find the Exact $\frac { \tan 70 ^ { \circ } - \tan ( - 50 ) ^ { \circ } } { 1 + \tan 70 ^ { \circ } \tan ( - 50 ) ^ { \circ } }$