Use Sum and Difference Formulas for Tangents
Find the exact value by using a difference identity.
-$$\frac { \tan 70 ^ { \circ } - \tan \left( - 50 ^ { \circ } \right) } { 1 + \tan 70 ^ { \circ } \tan \left( - 50 ^ { \circ } \right) }$$
A) $- \sqrt { 3 }$
B) $- \frac { \sqrt { 3 } } { 3 }$
C) $- \frac { 1 } { 2 }$
D) $- 2$ .

Question

Quizplus · Accepted Answer

The difference identity for tangent is:$$	an(a-b)=\frac{	an a-	an b}{1+	an a	an b}$$So,$$\frac{	an 70^\circ - 	an (-50^\circ)}{1 + 	an 70^\circ 	an (-50^\circ)} = 	an(70^\circ - (-50^\circ)) = 	an 120^\circ = -\sqrt{3}$$