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August 26th, 2009, 10:39 AM   #1
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De Moivre's formula and Newton's binomial formula

Using De Moivre's formula and Newton's binomial formula show that:

a)

b)

I really have no idea how to transform them using these formulas??
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August 26th, 2009, 03:50 PM   #2
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Re: De Moivre's formula and Newton's binomial formula

Quote:
Originally Posted by agro
Using De Moivre's formula and Newton's binomial formula show that:

a)

b)

I really have no idea how to transform them using these formulas??
It is straigtfoward but tediuous. I'll do the first. See if you can do the second. The main point is using the double angle formulas for sin and cos.
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August 26th, 2009, 04:42 PM   #3
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Re: De Moivre's formula and Newton's binomial formula

I think the idea here is to use De Moivre's formula, namely

Note that if then so De M.'s formula can be modified to



Therefore,



Expand out to get the required result.
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August 27th, 2009, 06:17 AM   #4
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Re: De Moivre's formula and Newton's binomial formula

Thanks! I managed to do the second part myself.
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