Express the product as a sum or difference.
-$\sin 7 x \cos 4 x$
A) $\frac { 1 } { 2 } ( \sin 11 x + \sin 3 x )$
B) $\sin \left( \cos 28 x ^ { 2 } \right)$
C) $\frac { 1 } { 2 } ( \cos 11 x - \cos 3 x )$
D) $\frac { 1 } { 2 } ( \sin 11 x + \cos 3 x )$

Question

Quizplus · Accepted Answer

The product-to-sum formula for sine and cosine is $\sin A \cos B = \frac{1}{2}(\sin(A + B) + \sin(A - B))$. Applying this formula to $\sin 7x \cos 4x$ gives $\frac{1}{2}(\sin(7x + 4x) + \sin(7x - 4x)) = \frac{1}{2}(\sin 11x + \sin 3x)$.

Express the Product as a Sum or Difference sin⁡7xcos⁡4x\sin 7 x \cos 4 xsin7xcos4x

Express the Product as a Sum or Difference $\sin 7 x \cos 4 x$