Use Identities to find the exact value.
-$\cos 255 ^ { \circ }$
A) $\sqrt { 2 } - \sqrt { 6 }$
B) $\frac { \sqrt { 2 } - \sqrt { 6 } } { 4 }$
C) $\sqrt { 6 } - \sqrt { 2 }$
D) $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$

Question

Quizplus · Accepted Answer

$\cos 255^\circ$ can be rewritten using the identity $\cos(360^\circ - x) = -\cos(x)$, so $\cos 255^\circ = -\cos(105^\circ)$. The exact value of $\cos 105^\circ$ can be found using the sum of angles formula: $\cos(60^\circ + 45^\circ) = \cos 60^\circ \cos 45^\circ - \sin 60^\circ \sin 45^\circ$, which simplifies to $-\frac{\sqrt{2} - \sqrt{6}}{4}$.

Use Identities to Find the Exact Value cos⁡255∘\cos 255 ^ { \circ }cos255∘

Use Identities to Find the Exact Value $\cos 255 ^ { \circ }$