Express the sum or difference as a product of sines and/or cosines.
-$\sin ( 8 \theta ) - \sin ( 4 \theta )$
A) $2 \sin ( 2 \theta )$
B) $2 \sin ( 2 \theta ) \cos ( 6 \theta )$
C) $2 \cos ( 4 \theta ) \cos ( 6 \theta )$
D) $2 \sin ( 6 \theta ) \cos ( 2 \theta )$

Question

Quizplus · Accepted Answer

The expression $\sin ( 8 \theta ) - \sin ( 4 \theta )$ can be rewritten using the sine difference identity: $\sin A - \sin B = 2 \cos \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right)$. Applying this identity with $A = 8\theta$ and $B = 4\theta$, we get $2 \cos(6\theta) \sin(2\theta)$, which matches choice B.

Express the Sum or Difference as a Product of Sines sin⁡(8θ)−sin⁡(4θ)\sin ( 8 \theta ) - \sin ( 4 \theta )sin(8θ)−sin(4θ)

Express the Sum or Difference as a Product of Sines $\sin ( 8 \theta ) - \sin ( 4 \theta )$