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# P2 Proof question! watch

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1. hey.. It's me again.
I promise this will be the last one

I'm a bit stumped as to what to do with this one:

given that tan(x/2) = t

prove that cos x = (1 - t^2) / (1 + t^2)

What do I do??
2. (Original post by kimoni)
hey.. It's me again.
I promise this will be the last one

I'm a bit stumped as to what to do with this one:

given that tan(x/2) = t

prove that cos x = (1 - t^2) / (1 + t^2)

What do I do??
substitute t into RHS, then sin/cos for tan and hopefully it should cancel down!
3. did u do it? i cant get it to cancel ffs lol
4. (Original post by hihihihi)
substitute t into RHS, then sin/cos for tan and hopefully it should cancel down!
aaaah! you legend, it works!!
needed a bit of the half angle formulae here.. nasty
5. (Original post by hihihihi)
did u do it? i cant get it to cancel ffs lol
Well, i just did what you said... subbed in t = tan 1/2 x
then for each tan used sin/cos identity

1 - sin^2[(1/2)x]/cos^2[(1/2)x] / 1 + sin^2[(1/2)x]/cos^2[(1/2)x]
(-yuck that looks horrible in linear format)

then use half angle formulae.. divide by flipping the bottom upside down.. cancels nicely

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