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.

<pre><font size = 4 color = "indigo"><b>
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</pre></b>