Holy smoke, that was fast!

I got it now.

I'm a little surprised you came up with the hint so fast.

For the equality to hold, d == 0 must be satisfied.

In fact, I'm considering a more general problem of manipulating

Code:

aN*sin(w)^N + .... + a3*sin(w)^3 + a1*sin(w)
------------------------------------------------ (1)
bN*cos(w)^N + .....+ b3*cos(w)^3 + b1*cos(w)

into

Code:

sin(w)^N sin(w)^3 sin(w)
cN*--------- + c3 ----------- + c1*-------- (2)
cos(w)^N cos(w)^3 cos(w)

Where N is odd.

I suspect your hint can be used for any N by using appropriate powers of you hints. I'll look into that.