Express the sum or difference as a product.
-$\sin 9 x + \sin 3 x$
A) $2 \sin 6 x \cos 3 x$
B) $2 \cos 6 x \sin 3 x$
C) $2 \sin 6 x \sin 3 x$
D) $2 \sin 12 x$

Question

Quizplus · Accepted Answer

The sum $\sin 9x + \sin 3x$ can be expressed as a product using the sum-to-product formula for sine, which is $\sin A + \sin B = 2 \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)$. Applying this formula with $A = 9x$ and $B = 3x$, we get $2 \sin 6x \cos 3x$.

Express the Sum or Difference as a Product sin⁡9x+sin⁡3x\sin 9 x + \sin 3 xsin9x+sin3x

Express the Sum or Difference as a Product $\sin 9 x + \sin 3 x$