Find the exact value of the expression.
-$\sin 255 ^ { \circ } \cos 15 ^ { \circ } - \cos 255 ^ { \circ } \sin 15 ^ { \circ }$
A) $- \frac { \sqrt { 3 } } { 2 }$
B) $- \frac { 17 } { 4 }$
C) $- \frac { 1 } { 2 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

This expression is an application of the sine difference identity, $\sin(a - b) = \sin a \cos b - \cos a \sin b$. Applying this identity with $a = 255^\circ$ and $b = 15^\circ$, we get $\sin(255^\circ - 15^\circ) = \sin(240^\circ)$. The exact value of $\sin(240^\circ)$ is $-\frac{\sqrt{3}}{2}$, which corresponds to choice A.

Find the Exact Value of the Expression sin⁡255∘cos⁡15∘−cos⁡255∘sin⁡15∘\sin 255 ^ { \circ } \cos 15 ^ { \circ } - \cos 255 ^ { \circ } \sin 15 ^ { \circ }sin255∘cos15∘−cos255∘sin15∘

Find the Exact Value of the Expression $\sin 255 ^ { \circ } \cos 15 ^ { \circ } - \cos 255 ^ { \circ } \sin 15 ^ { \circ }$