hi all ,

 

i can't figure out how i am ment to use the stated fact about tan x.

 

the way i'd do it is dividing the series expansion for cos(x) into that for sin(x)... but yeah i dunno

 

any advice would be greatly appreciated

 

__sarah__

there is second part to this question, and again i could do it by other means, but not using the given fact

 

this is the second part to the question:

(a) You are given two things. The FIRST thing that would come to my mind is to substitute the first into the second ...

 

(b) Having said (a), I shouldn't say anything more.

 

Sarah, these are nothing more than direct substitution problems.

but part a says to use the first fact, not the second (or both) ... or are you talking about doing part b?

sorry to be such a panicky hassle sort of thing, this si just about the most stresfull week so far this year!

(a) You are given 2 things :

 

1. tan(x) is analytic in (-pi/2, pi/2)

2. tan(x) is odd

 

Substitute the expansion (from 1) in the equation for 2.

ok i have so i get

 

tan'(x)= 1 + tan^{2}(-x)

 

but i dont see how this helps... (although i am sure it does )

oh wait its like an identity or something, 1 + tan^{2} = sec^{2) or something like that, damn i wish i had textbook with me right now

I was talking about part (a), not part (b)

 

Apply the power series expansion to each side of the given equation (the "fact"). What do you get ?

this?

 

i gotta run though i'll be back in a few hours...sorry

Picture 1.pdf

or is it this...because this makes more sense to me....

Picture 2.pdf

oh ok then you expand it like this....

 

 

therefore all n even terms are zero (assuming you start from n = 1 right?)

 

lol....now for part b! dammit

How do you show that the even terms are zero ? It does not matter what value of n you start from, for the even terms to vanish (but in any case, you start with n=0 because that term is part of a general power series).

when i said

 

"oh ok then you expand it like this...."

 

i ment to post this along with it...

i tried a similar method for part (b) but i don't know how to expand the square of a infinite sum...

ok so i have got this much so far for part (b), but as i said before i then get a infinte sum squared and i don't know how to deal with such a thing!

(a) You have a tiny error in post #14. Why did a_0 change signs on the RHS ?

 

(b) You are not asked for all the coefficients, right ? So, just write out the first few terms (I'll let you figure out how many you need to write), square it, and compare coefficients.

you mean end up with things such as

 

(a_1)^{2} = 3(a_3)

 

??

I couldn't comment on that unless I know how you got it.

oh sorry, yep hang on...

(a) You have a tiny error in post #14. Why did a_0 change signs on the RHS ?

 

oh ok so a_0 is zero aswell (like all the even n terms)?

ok so post #14 should have been this....

ok so this is what i do to expand it, but then well yep i don't know how you would compare terms with this... :S

wait second....may have eureka moment here....!!!

ok got it i think, i was on the right track........here we go !