Use Sum and Difference Formulas for Tangents
Find the exact value by using a difference identity.
-$\tan 255 ^ { \circ }$
A) $\sqrt { 3 } + 2$
B) $- \sqrt { 3 } + 2$
C) $- \sqrt { 3 } - 2$
D) $\sqrt { 3 } - 2$

Question

Quizplus · Accepted Answer

The exact value of $\tan 255^\circ$ can be found using the difference identity $\tan (a - b) = \frac{\tan a - \tan b}{1 + \tan a \tan b}$ with $a = 270^\circ$ and $b = 15^\circ$, knowing that $\tan 270^\circ = 0$ and $\tan 15^\circ = 2 - \sqrt{3}$, leading to $\tan 255^\circ = \sqrt{3} + 2$.

Use Sum and Difference Formulas for Tangents Find the Exact tan⁡255∘\tan 255 ^ { \circ }tan255∘

Use Sum and Difference Formulas for Tangents
Find the Exact $\tan 255 ^ { \circ }$