FP2 Prove by induction...

FP2 Jan 07 AQA Q7 for anyone interested!
Right, I have (cosx+isinx)ⁿ=cosnx+isinnx
I assume n=k and it works for n=1.
The problem is I cant make the sides equal for n=k+1
So far I have...
(Cosx+isinx)^k+1
=(coskx+isinkx)(cosx+isinx)
Which is correct in the mark scheme, then you multiply out and the final answer must be cos(k+1)x+isin(k+1)x.
My problem is when multiplying out, how do I make this work.
Does coskxisinx+isinkxcosx cancel out somehow or equal zero somehow? So confused! :s-smilie:

Thank you

(edited 13 years ago)

Reply 1

Clarity Incognito

11

Original post by ChappersBC

FP2 Jan 07 AQA Q7 for anyone interested!
Right, I have (cosx+isinx)ⁿ=cosnx+isinnx
I assume n=k and it works for n=1.
The problem is I cant make the sides equal for n=k+1
So far I have...
(Cosx+isinx)^k+1
=(coskx+isinkx)(cosx+isinx)
Which is correct in the mark scheme, then you multiply out and the final answer must be cos(k+1)x+isin(k+1)x.
My problem is when multiplying out, how do I make this work.
Does coskxisinx+isinkxcosx cancel out somehow or equal zero somehow? So confused! :s-smilie:

Thank you

Think of your addition formulae.