Question

Express sin6θ + sin4θ as a product.

Answer 1

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

Explanation:

According to the trigonometric identities we have the following formula:

`sin (x) + sin (y)=2 sin((x+y)/(2)) cos((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((6\theta+4\theta)/(2)) cos((6\theta-4\theta)/(2))`

`sin (6\theta)+ sin (4\theta)=2 sin((10\theta)/(2)) cos((2\theta)/(2))`

Finally:

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