Math Is Fun Forum

ant

Member

Registered: 2006-06-07

Posts: 9

Going crazy over simple question

Ive got this question and the parts make sense but it doesnt work when i put it together. im not sure if that made sense, so ill just go straight to the question...

Prove:

1 - cos2x   
---------  =  tan²x
1 + cos2x

So i can do this part, using different expansions of cos2x

Then it says

Use this to prove that   tan π/8  = √2  -1
If you put this in a calculator it's true, and we just proved that the other two expressions were equal.
But when i sub in π/8 for x in the cos expression, i get 2 - 2√2  -1 , which is definately not equal to √2  -1.

so i dont know what im doing wrong, cos it seems so simple, but it's not working!

can anyone help?

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If you're not part of the solution, you're part of the precipitate.

ryos

Member

Registered: 2005-08-04

Posts: 394

Re: Going crazy over simple question

No, that's right. Remember that your cos expression is equal to tan²x. So, square (√2 - 1) and see if it comes out:
(√2 - 1)² = 2 - √2 - √2 + 1 = 2 - 2√2 + 1

Well, Ok, it didn't come out 100% -- the final expression ends in +1, not -1. Is that just a typo/other error?

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El que pega primero pega dos veces.