Poly: Deducing Trig stuff (1 Viewer)

[Starcraftmazter]

Question:
a) Use De Moivre's theorem to express cos 3theta in terms of cos theta and sin 3theta in terms of sin theta.

b) Use the result to solve the question 8x^3 - 6x+1=0

c) Deduce that

i) Cos (2pi/9) + cos (4pi/9) = cos (pi/9)
ii) cos (pi/8) . cos (3pi/8) . cos (5pi/8) . cos (7pi/8) = 1/8


Now I can do (a) and (b) easily (so don't waste time posting solutions to them!), but rather lost when I came to part (c). We did one example on that type of question with tan 5th, and after looking back at it briefly I understood the process fairly well, but maybe not because I couldn't do part (c) of that question. I ended up with something like this from memory:

Letting c = cos th,

cos 3th = 4c^3 - 3c = -1

And let th = pi/3, and hence th = pi/3 +- kpi/3

And then I didn't know how to get from there to what I should get at, so clearly I must be doing something wrong.


So, can someone post a solution that part (c) of the question above please? And if you understand what I did, maybe tell me where I went wrong (though I'm assuming everywhere )

 

[pLuvia]

Think about the sums of roots, and product of roots

 

[Starcraftmazter]

For the cosine eg, I have no clue how that can be applied. I havent looked at the 2nd part with the secs.

 

[noobking]

from a) and b), u get cos2pi/9, cos4pi/9 and cos 8pi/9 as the roots. by using the fact that cos8pi/9=-cospi/9 and sum of roots u will get the answer