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ninetypercent

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^ yes and no. typical exam questions will have part (i) to show the identity and then in part (ii) you use it
 
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Anyway, new question:



"hscishard" and "bored of fail", you're not allowed to answer this :p
 

Drongoski

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^ yes and no. typical exam questions will have part (i) to show the identity and then in part (ii) you use it
Yes = not directly. But if I were doing Ext 2 I will try to add it to my arsenal. Useful in some of the messier derivations in conics (see P89, Cambridge 4U book)
 

jyu

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New question:

Show
(sinx+sin3x+sin5x+sin7x+sin9x)/(cosx+cos3x+cos5x+cos7x+cos9x) = tan5x
This question does not require the use of those formulas.
 
Last edited:

AAEldar

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Anyway, new question:



"hscishard" and "bored of fail", you're not allowed to answer this :p
I'll give it a crack. I remember seeing your solution/hscishard's solution (whichever one of you uploaded the handwritten answer) but can't really remember it LOL. Might not end well.
 

jyu

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Factorise: 1-(sinx)^10=(1-(sinx)^2)(1+(sinx)^2+(sinx)^4+(sinx)^6+(sinx)^8)
=(cosx)^2 (1+(sinx)^2+(sinx)^4+(sinx)^6+(sinx)^8)

integ (cosx)(1+(sinx)^2+(sinx)^4+(sinx)^6+(sinx)^8) dx

let u=sinx etc.

integ (1+u^2+u^4+u^6+u^8) du etc.
 

Trebla

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Nice work...though I was hoping someone would pick it up more in the lines of a geometric series

 

Drongoski

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Nice work...though I was hoping someone would pick it up more in the lines of a geometric series


Trebla

Interesting question & beautiful solution. I thought I knew how to integrate. Ends up similar to jyu's.
 

jyu

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very likely with a hinting question beforehand
 

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