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# Further trigonometry FP3 watch

1. Hi, I'm stuck on the first question (1a) of excersize 7C. The question is:
Show that:

The examples on the pages before are all about sums of infinite geometric series which I understood, but I'm not really sure how this question relates to the example in any way.

Help would be appreciated
2. Well you can write the LHS as . As a hint, think Pascal's triangle... how can you factorise this expression?
3. Ah ye, I'm thinking its something to the power 4, because of those binomial coefficients. Is it (1+e^2ix)^4?
4. (Original post by jamie092)
Ah ye, I'm thinking its something to the power 4, because of those binomial coefficients. Is it (1+e^2ix)^4?
Yup, so you have to find the real part of .
5. (Original post by nuodai)
Yup, so you have to find the real part of .
Surely thats just ?
6. (Original post by jamie092)
Surely thats just ?
Nope, in general it's not true that so you can't just take the "Re" inside the brackets.
7. (Original post by nuodai)
Nope, in general it's not true that so you can't just take the "Re" inside the brackets.
Oh ye ofcourse ;<
Well now I'm stumped =(
8. (Original post by jamie092)
Oh ye ofcourse ;<
Well now I'm stumped =(
Well if then . You'll notice that the terms with even powers of y are real, and the terms with odd powers of y are imaginary (because of how the powers of i work). So set and expand as above. A bit of tedious algebraic manipulation should give you the right answer.
9. (Original post by nuodai)
Well if then . You'll notice that the terms with even powers of y are real, and the terms with odd powers of y are imaginary (because of how the powers of i work). So set and expand as above. A bit of tedious algebraic manipulation should give you the right answer.
ok thanks I'll give it a go

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