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(edited 6 years ago)
Original post by UCASLord
I'm having trouble understanding why
Unparseable latex formula:

cos^2^n(x) = (1 + cos^n(x))



I am aware of the 1 = sin^2x + cos^2x identity, but I don't see how it fits into here, if indeed it does.


...

hope that helps :u:
Original post by UCASLord
I'm having trouble understanding why cos^2^n(x) = (1 + cos^n(x))

I am aware of the 1 = sin^2x + cos^2x identity, but I don't see how it fits into here, if indeed it does.



Do you mean cos⁡2n(x)=1+cos⁡n(x)\cos^{2n}(x)=1+\cos^n(x)??

Well that's not true as at x=0x=0 you have LHS=1 and RHS =2
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UCASLord
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(edited 6 years ago)
Original post by UCASLord
Sorry, I meant this:

Why does cos^n(x) + cos^2n(x) = cos^n(x)(1 + cos^n(x))


u=cos(x)u=cos(x)

un+u2n=un(1+un)u^n+u^{2n}=u^n(1+u^n)

∴cosnx+cos2nx=cosnx(1+cosnx)\therefore cos^nx+cos^{2n}x=cos^nx(1+cos^nx)
Original post by UCASLord
Sorry, I meant this:

Why does cos^n(x) + cos^2n(x) = cos^n(x)(1 + cos^n(x))


Because you can factor out a cos⁡n(x)\cos^n(x) from the LHS.
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UCASLord
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(edited 6 years ago)

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