Question 800689
<pre>
We will use the identities

cos(2<font face="symbol">q</font>) = 1-2sinē(<font face="symbol">q</font>)
sin(2<font face="symbol">q</font>) = 2sin(<font face="symbol">q</font>)cos(<font face="symbol">q</font>)
cosē(<font face="symbol">q</font>) = 1-sinē(<font face="symbol">q</font>)

cos(4x) - 4cos(2x) + 3

1-2sinē(2x) - 4[1-2sinē(x)] + 3

1 - 2[2sin(x)cos(x)]ē - 4 + 8sinē(x) + 3

The numbers combine to 0, so we have:

-2[2sin(x)cos(x)]ē + 8sinē(x)

-2[4sinē(x)cosē(x)] + 8sinē(x)

-8sinē(x)cosē(x) + 8sinē(x)

-8sinē(x)[1-sinē(x)] + 8sinē(x)

-8sinē(x)+8sin<sup>4</sup>(x) + 8sinē(x)

8sin<sup>4</sup>(x)

Edwin</pre>