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

Question

Quizplus · Accepted Answer

$\cos 255^\circ$ can be rewritten using the identity $\cos(180^\circ + \theta) = -\cos \theta$, where $\theta = 75^\circ$. $\cos 75^\circ$ can be found using the half-angle formula or sum/difference identities, such as $\cos(30^\circ + 45^\circ)$. This results in $\cos 75^\circ = \frac{\sqrt{6} - \sqrt{2}}{4}$. Since $\cos 255^\circ = -\cos 75^\circ$, the answer is $\frac{\sqrt{2} - \sqrt{6}}{4}$.

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

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