Question

Express sin6θ + sin4θ as a product.

Answer 1

Answer: $2 sin(5 \theta) cos \theta$

Step-by-step explanation:

According to the trigonometric identities we have the following formula:

$sin (x) + sin (y)=2 sin(\frac{x+y}{2}) cos(\frac{x-y}{2})$

Now, we have the following:

$sin (6\theta)+ sin (4\theta)$

Where $x=6\theta$ and $y=4\theta$

Hence:

$sin (6\theta)+ sin (4\theta)=2 sin(\frac{6\theta+4\theta}{2}) cos(\frac{6\theta-4\theta}{2})$

$sin (6\theta)+ sin (4\theta)=2 sin(\frac{10\theta}{2}) cos(\frac{2\theta}{2})$

Finally:

$sin (6\theta)+ sin (4\theta)=2 sin(5\theta) cos(\theta)$