Use Sum and Difference Formulas for Tangents
Find the exact value by using a difference identity.
-$$\frac { \tan 175 ^ { \circ } - \tan 55 ^ { \circ } } { 1 + \tan 175 ^ { \circ } \tan 55 ^ { \circ } }$$
A) $- \sqrt { 3 }$
B) $- \frac { \sqrt { 3 } } { 3 }$
C) $- \frac { 1 } { 2 }$
D) $- 2$

Question

Quizplus · Accepted Answer

The given expression is in the form of the tangent difference identity, $\tan(\alpha - \beta) = \frac{\tan \alpha - \tan \beta}{1 + \tan \alpha \tan \beta}$. Here, $\alpha = 175^\circ$ and $\beta = 55^\circ$, so it simplifies to $\tan(175^\circ - 55^\circ) = \tan(120^\circ)$. The exact value of $\tan(120^\circ)$ is $-\sqrt{3}$, since $120^\circ$ is in the second quadrant where tangent is negative, and it's the tangent of $60^\circ$ reflected, which is $\sqrt{3}$.

Use Sum and Difference Formulas for Tangents Find the Exact tan⁡175∘−tan⁡55∘1+tan⁡175∘tan⁡55∘\frac { \tan 175 ^ { \circ } - \tan 55 ^ { \circ } } { 1 + \tan 175 ^ { \circ } \tan 55 ^ { \circ } }1+tan175∘tan55∘tan175∘−tan55∘​

Use Sum and Difference Formulas for Tangents
Find the Exact $\frac { \tan 175 ^ { \circ } - \tan 55 ^ { \circ } } { 1 + \tan 175 ^ { \circ } \tan 55 ^ { \circ } }$