Express the sum or difference as a product of sines and/or cosines.
-$\sin ( 2 \theta ) - \sin ( 4 \theta )$
A) $2 \cos ( 2 \theta ) \cos ( 3 \theta )$
B) $- 2 \sin \theta$
C) $- 2 \sin \theta \cos ( 3 \theta )$
D) $2 \sin ( 3 \theta ) \cos \theta$

Question

Quizplus · Accepted Answer

Using the identity $\sin A - \sin B = 2 \cos \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)$, we get $\sin(2\theta) - \sin(4\theta) = 2 \cos(3\theta) \sin(-\theta) = -2 \sin(\theta) \cos(3\theta)$.

Express the Sum or Difference as a Product of Sines sin⁡(2θ)−sin⁡(4θ)\sin ( 2 \theta ) - \sin ( 4 \theta )sin(2θ)−sin(4θ)

Express the Sum or Difference as a Product of Sines $\sin ( 2 \theta ) - \sin ( 4 \theta )$