Write the sum as a product. $\sin 4 x + \sin 5 x$
A) $\sin 4 x \sin 5 x$
B) $\sin 4 x \cos 5 x$
C) $2 \sin ( 9 x / 2 ) \cos ( x / 2 )$
D) $\sin 4 x \cos ( x / 2 )$
E) $2 \sin 3 x \cos ( x / 2 )$

Question

Quizplus · Accepted Answer

We can use the identity $\sin a + \sin b = 2 \sin \left(\frac{a+b}{2}ight) \cos \left(\frac{a-b}{2}ight)$ to rewrite the sum as:

$$\sin 4x + \sin 5x = 2 \sin \left(\frac{4x+5x}{2}ight) \cos \left(\frac{5x-4x}{2}ight) = 2 \sin \left(\frac{9x}{2}ight) \cos \left(\frac{x}{2}ight)$$

So the answer is $\boxed{	ext{(C) }2\sin\left(\frac{9x}{2}ight)\cos\left(\frac{x}{2}ight)}$.

Write the Sum as a Product sin⁡4x+sin⁡5x\sin 4 x + \sin 5 xsin4x+sin5x

Write the Sum as a Product $\sin 4 x + \sin 5 x$