Use a sum or difference identity to find the exact value.
-$\sin 25 ^ { \circ } \cos 95 ^ { \circ } + \cos 25 ^ { \circ } \sin 95 ^ { \circ }$
A) $- \frac { 1 } { 2 }$
B) $- \frac { \sqrt { 3 } } { 2 }$
C) $\frac { 5 } { 12 }$
D) $\frac { \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

This expression can be simplified using the sum identity for sine: $\sin(A + B) = \sin A \cos B + \cos A \sin B$. Applying this identity with $A = 25^\circ$ and $B = 95^\circ$, we get $\sin(25^\circ + 95^\circ) = \sin(120^\circ)$, which equals $\frac{\sqrt{3}}{2}$.

Use a Sum or Difference Identity to Find the Exact sin⁡25∘cos⁡95∘+cos⁡25∘sin⁡95∘\sin 25 ^ { \circ } \cos 95 ^ { \circ } + \cos 25 ^ { \circ } \sin 95 ^ { \circ }sin25∘cos95∘+cos25∘sin95∘

Use a Sum or Difference Identity to Find the Exact $\sin 25 ^ { \circ } \cos 95 ^ { \circ } + \cos 25 ^ { \circ } \sin 95 ^ { \circ }$