Answer: [tex]2 sin(5 \theta) cos \theta[/tex]
Step-by-step explanation:
According to the trigonometric identities we have the following formula:
[tex]sin (x) + sin (y)=2 sin(\frac{x+y}{2}) cos(\frac{x-y}{2})[/tex]
Now, we have the following:
[tex]sin (6\theta)+ sin (4\theta)[/tex]
Where [tex]x=6\theta[/tex] and [tex]y=4\theta[/tex]
Hence:
[tex]sin (6\theta)+ sin (4\theta)=2 sin(\frac{6\theta+4\theta}{2}) cos(\frac{6\theta-4\theta}{2})[/tex]
[tex]sin (6\theta)+ sin (4\theta)=2 sin(\frac{10\theta}{2}) cos(\frac{2\theta}{2})[/tex]
Finally:
[tex]sin (6\theta)+ sin (4\theta)=2 sin(5\theta) cos(\theta)[/tex]
