Express the product as a sum or difference.
-$\sin 5 x \cos 6 x$
A) $\frac { 1 } { 2 } ( \sin 11 x - \sin x )$
B) $\frac { 1 } { 2 } ( \cos 11 x + \sin x )$
C) $\frac { 1 } { 2 } ( \cos 11 x - \cos x )$
D) $\sin \left( \cos 30 x ^ { 2 } \right)$

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 to $\sin 5x \cos 6x$, we get $\frac{1}{2}[\sin(11x) + \sin(-x)]$, which simplifies to $\frac{1}{2}(\sin 11x - \sin x)$.

Express the Product as a Sum or Difference sin⁡5xcos⁡6x\sin 5 x \cos 6 xsin5xcos6x

Express the Product as a Sum or Difference $\sin 5 x \cos 6 x$