Express the sum or difference as a product.
-$$\sin \frac { 9 x } { 2 } + \sin \frac { 5 x } { 2 }$$
A) $2 \sin \frac { 7 x } { 2 } \cos x$
B) $2 \sin \frac { 7 x } { 2 } \sin x$
C) $2 \cos 7 x \sin x$
D) $2 \sin 7 x$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the sum-to-product identities. Specifically, the identity $\sin A + \sin B = 2 \sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right)$ is applicable here. Substituting $A = \frac{9x}{2}$ and $B = \frac{5x}{2}$ into this identity gives $2 \sin \left( \frac{9x + 5x}{4} \right) \cos \left( \frac{9x - 5x}{4} \right) = 2 \sin \frac{7x}{2} \cos x$, which matches option A.

Express the Sum or Difference as a Product sin⁡9x2+sin⁡5x2\sin \frac { 9 x } { 2 } + \sin \frac { 5 x } { 2 }sin29x​+sin25x​

Express the Sum or Difference as a Product $\sin \frac { 9 x } { 2 } + \sin \frac { 5 x } { 2 }$