Question

sin(4x)=8 sin(x)cos^3(x)-4 sin(x)cos(x)

Proofs are beyond confusing...

Answer 1

sounds like you are trying to show this is an identity

Answer 2

Which I am trying to figure out now lol

Answer 3

it looks like i should be using 2 sin theta and cos theta

Answer 4

is the above written correctly?

Answer 5

seems like there could be a cube or something missing

Answer 6

yeah it suppose to be cosine cubed which i have there

Answer 7

well see if you can continue from here
\[8 \sin(x) \cos^3(x)-4 \sin(x)\cos(x) \\ \text{ I would start by factoring out } 4 \sin(x)\cos(x) \\ 4 \sin(x) \cos(x)[\cos^2(x)-1] \\ 2 \cdot 2 \sin(x)\cos(x)[-1(1-\cos^2(x))] \]

Answer 8

like right here I see a couple of identities you can use

Answer 9

oops missed a 2

Answer 10

\[8 \sin(x) \cos^3(x)-4 \sin(x)\cos(x) \\ \text{ I would start by factoring out } 4 \sin(x)\cos(x) \\ 4 \sin(x) \cos(x)[2\cos^2(x)-1] \\ 2 \cdot 2 \sin(x)\cos(x)[-1(1-2 \cos^2(x))] \]

Answer 11

beautiful :)

Answer 12

for example guess what 2sin(x)cos(x)
or guess what 2cos^2(x)-1 or if you like -1(1-2cos^2(x)) equals

Answer 13

http://www.eeweb.com/tools/math-sheets/images/trigonometry-laws-and-identities-small.png
look under double angle identities if you do not recall

Answer 14

This is what I did

Answer 15

so is this right?

Answer 16

I like the last 5 lines
and the first 2 lines looks like you factored as I did above just didn't end the ( parenthesis thing on the second line

Answer 17

or on the first line

Answer 18

\[8 \sin(x) \cos^3(x)-4 \sin(x)\cos(x) \\ \text{ I would start by factoring out } 4 \sin(x)\cos(x) \\ 4 \sin(x) \cos(x)[2\cos^2(x)-1] \\ \]

but yeah that is essentially what I have above

Answer 19

you just need some ( ) in there

Answer 20

this is exactly what I would do to fix your ( ) issue:
\[4 \sin(x)\cos(x)(2\cos^2(x)-1) \text{ for first line; just drop that one \between the } \\ 4 \text{ and } \sin(x) \\ \\\]

Answer 21

the second line ...
I would change that first ( to a *
and then also put ( ) around the 2cos^2(x)-1
like so:
\[2 \cdot 2 \sin(x)\cos(x)(2 \cos^2(x)-1)\]

Answer 22

Thanks soo much again!! I swear so much work under one problem lol @freckles