SOLUTION: Verify this identity : sin4x = (cosx)(4sinx-8sin^3x) Here is what I've shamefully accomplished so far : =(cosx)4sinx(1-2sin^2x) =(cosx)4sinx(cos2x) =(cos3x)(4sinx) =???

Algebra ->  Trigonometry-basics -> SOLUTION: Verify this identity : sin4x = (cosx)(4sinx-8sin^3x) Here is what I've shamefully accomplished so far : =(cosx)4sinx(1-2sin^2x) =(cosx)4sinx(cos2x) =(cos3x)(4sinx) =???      Log On


   

Question 167730: Verify this identity :
sin4x = (cosx)(4sinx-8sin^3x)
Here is what I've shamefully accomplished so far :
=(cosx)4sinx(1-2sin^2x)
=(cosx)4sinx(cos2x)
=(cos3x)(4sinx)
=???????
Now I'm stuck! Any insight would be appreciated greatly! Thank you in advance for your time!!
Desperately seeking solution, Rebecca
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given equation


... Factor out (good so far)


Rearrange the terms.


Factor 4 into 2*2


Use the identity


Use the identity


Let z=2x


Substitute "z" in for 2x


Use the identity (similar to the previous used identity just with a different variable)



Plug in z=2x


Multiply


Since both sides of the equation are equal, this means that we've verified the identity