Question

Why does 2sin(x) * cos(x) = sin (2x)?

Answer 1

It doesn't...?

Answer 2

It doesn't? I'm supposed to prove that it does:

Answer 3

its that one identity

Answer 4

Oh, sorry. I misread the question. My appologies

Answer 5

I read it as = 2sin (x)

don't know what I was thinking lol

Answer 6

I typed it as 2sin (x) by accident, I just edited the original question sorry lol

Answer 7

oh, lol. so I'm not going crazy

Answer 8

nah, you aren't. but I'm supposed to prove that it does, but it doesn't make sense to me,

Answer 9

Why not?

Answer 10

Because it goes from 2sin(x)cos(x) to just sin (2x), where did the cos(x) go?

Answer 11

hint* \[\large sin(2x) = sin(x+x)\]

What can you do with that?

Answer 12

Replying because I want to know the answer too.

Answer 13

(x + x) is 2x so sin(2x) = sin(2x)

Answer 14

Another hint* Remember the addition formula? Being something along the lines of \(\large sin(A+B) = ?\)

Answer 15

As JohnWeldon said, you can change sin(2x) into sin (x + x)
Remember formula
sin (A + B) = sin A cos B + cos A sin B

Answer 16

It's still not making sense to me, I've read the addition formula, but none of this was really taught to me by anyone so I don't know any of it

Answer 17

Don't worry about it!

So you know there is an addition formula...which as shown above is:
\[\large sin(A+B) = sin(A)cos(B) + sin(B)cos(A)\]

So if we apply that here...

\[\large sin(x+x) = sin(x)cos(x) + sin(x)cos(x)\]

and from there.....

Answer 18

OH. I see it. sin (x + x) is just sin (2x) which equals sin(x)cos(x) + sin(x)cos(x). Okay, I finally get it. Thank you!

Answer 19

Exactly! And not a problem!