SOLUTION: Verify that this equation is an identity... sin(4y) = 4sin(y)cos(y) - 8sin³(y) I tried working on the right side and this is as far as I got. First I factored... 4sinycosy(1 -

Algebra ->  Trigonometry-basics -> SOLUTION: Verify that this equation is an identity... sin(4y) = 4sin(y)cos(y) - 8sin³(y) I tried working on the right side and this is as far as I got. First I factored... 4sinycosy(1 -       Log On


   

Question 188283: Verify that this equation is an identity...
sin(4y) = 4sin(y)cos(y) - 8sin³(y)
I tried working on the right side and this is as far as I got.
First I factored...
4sinycosy(1 - 2sin^2y)
then I substituted 1-cos^2y for sin^y
4sinycosy(1-2(1-cos^2y)
4sinycisy(1-2+2cos^2y)
4sinycosy(2cos^2y-1)
and I don't know what to do next to get 4siny
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
Verify that this equation is an identity...
sin(4y) = 4sin(y)cos(y) - 8sin³(y)
I tried working on the right side and this is as far as I got. 

Although the right side looks more complicated than
the left side, it isn't, because 4y is much more 
complicated than just y. 

So you'd do better to start with the left side and 
use these two double-angle formulas:

sin(2@) = 2sin(@)cos(@)  and   cos(2@) = 1 - 2sin²(@)

----------------------------------------------------

sin(4y)

sin[2(2y)]

2sin(2y)cos(2y)

2[2sin(y)cos(y)][1 - 2sin²(y)]

4sin(y)cos(y)[1 - 2sin²(y)]

4sin(y)cos(y) - 8sin³(y)

Edwin