Question

Select the next logical step or pair of steps in a proof of this identity. (picture below) I just learned this but I'd like to get more in depth (i'm just using my textbook and it's kinda hard without a teacher here :p any help is appreciated!)

Answer 1

I know the double identities I'm just not sure how to apply any here especially since there's a 4 in front of sin theta instead of a 2 like in my textbook

Answer 2

The first one.

Answer 3

If you don't mind, can you show me how you got it? (: It doesn't have to be now, I'm sure it's long.

Answer 4

Thanks btw (:

Answer 5

\[4\cos \theta \sin \theta-8\cos \theta \sin ^3\theta \]
Factor out 4cos theta sin theta:
\[4\cos \theta \sin \theta(1-2\sin ^2\theta)\]
Now we know that sin2 theta = 2sin theta cos theta
So :
\[4\cos \theta \sin \theta=4\sin \theta \cos \theta=2(2\sin \theta \cos \theta)=4\sin \beta \cos \theta\]

Answer 6

Ohh, I can see the factoring now. that's what had confused me

Answer 7

well, the most

Answer 8

\[4\cosθ\sinθ=4\sinθ\cosθ=2(2\sinθ\cosθ)=2\sin 2\]theta

Answer 9

Thank you (:

Answer 10

yw