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.Com
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) (Show Source): You can put this solution on YOUR website!
=cos(x)(4sin(x)-8sin^3(x)) )
... Start with the given equation
=cos(x)4sin(x)(1-2sin(x)) )
... Factor out )
(good so far)
=4sin(x)cos(x)(1-2sin(x)) )
Rearrange the terms.
=2*2sin(x)cos(x)(1-2sin(x)) )
Factor 4 into 2*2
=2sin(2x)(1-2sin(x)) )
Use the identity cos(x)=sin(2x))
=2sin(2x)cos(2x) )
Use the identity =cos(2x))
Let
=2sin(z)cos(z) )
Substitute "z" in for 2x
=sin(2z) )
Use the identity cos(z)=sin(2z))
(similar to the previous used identity just with a different variable)
=sin(2*2x) )
Plug in
=sin(4x) )
Multiply
Since both sides of the equation are equal, this means that we've verified the identity
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