Express the sum or difference as a product.
-$\sin 75 ^ { \circ } + \sin 15 ^ { \circ }$
A) $\frac { \sqrt { 6 } } { 2 }$
B) $\frac { \sqrt { 6 } } { 4 }$
C) $\frac { \sqrt { 3 } } { 2 }$
D) $- \frac { \sqrt { 6 } } { 2 }$

Question

Quizplus · Accepted Answer

The sum $\sin 75 ^ { \circ } + \sin 15 ^ { \circ }$ can be expressed as a product using the sine sum-to-product identity: $\sin x + \sin y = 2 \sin \left( \frac{x + y}{2} \right) \cos \left( \frac{x - y}{2} \right)$. Substituting $x = 75^\circ$ and $y = 15^\circ$, we get $2 \sin \left( \frac{75 + 15}{2} \right) \cos \left( \frac{75 - 15}{2} \right) = 2 \sin(45^\circ) \cos(30^\circ)$, which simplifies to $2 \cdot \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} = \frac{\sqrt{6}}{2}$.

Express the Sum or Difference as a Product sin⁡75∘+sin⁡15∘\sin 75 ^ { \circ } + \sin 15 ^ { \circ }sin75∘+sin15∘

Express the Sum or Difference as a Product $\sin 75 ^ { \circ } + \sin 15 ^ { \circ }$