Use Sum and Difference Formulas for Tangents
Find the exact value by using a difference identity.
-$\frac { \tan 25 ^ { \circ } + \tan 5 ^ { \circ } } { 1 - \tan 25 ^ { \circ } \tan 5 ^ { \circ } }$
A) $\frac { \sqrt { 3 } } { 3 }$
B) $\sqrt { 3 }$
C) $\frac { 1 } { 2 }$
D) 2

Question

Quizplus · Accepted Answer

The given expression can be simplified using the tangent sum formula: $\tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}$. Here, $\alpha = 25^\circ$ and $\beta = 5^\circ$, so the expression simplifies to $\tan(25^\circ + 5^\circ) = \tan(30^\circ)$. The exact value of $\tan(30^\circ)$ is $\frac{\sqrt{3}}{3}$.

Use Sum and Difference Formulas for Tangents Find the Exact tan⁡25∘+tan⁡5∘1−tan⁡25∘tan⁡5∘\frac { \tan 25 ^ { \circ } + \tan 5 ^ { \circ } } { 1 - \tan 25 ^ { \circ } \tan 5 ^ { \circ } }1−tan25∘tan5∘tan25∘+tan5∘​

Use Sum and Difference Formulas for Tangents
Find the Exact $\frac { \tan 25 ^ { \circ } + \tan 5 ^ { \circ } } { 1 - \tan 25 ^ { \circ } \tan 5 ^ { \circ } }$