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Trignometry

Cool goIITian

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31 May 2007 21:48:25 IST

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triogonometric problem

None

2cosA= x + 1/x
find the value of x^3 + 1/x^3

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Comments (6)

joy francis

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Joined: 19 Feb 2007

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31 May 2007 21:56:31 IST

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can you provide the options please

Akansha

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31 May 2007 22:01:35 IST

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(x+1/x)^3=x^3+1/x^3+3(x+1/x)

x^3+1/x^3=8cos^3A-6cosA=2(4cos^3A-3cosA)=2cos3A

-1<=cos3A<=1

--------> (x^3+1/x^3)

[-2,2]

PLS TELL IF ITS CORRECT OR NOT

boredom

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31 May 2007 22:04:30 IST

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hey,

if 2cosA=x=1/x,

then x^3=1/x^3= x^3+1/x^3=(x=1/x)^3-3x-3/x (3x^2/x+ 3x/x^2)

hence, =(x+1/x)^3-3(x+1/x),

(2cosA)^3-3*2cosA

=8cos³A-6cosA

rajan edu

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31 May 2007 23:41:51 IST

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The answer is not known but x^2 + 1/x^2 , X^3 + 1/x^3 and X^4 + 1/x^4 all have a form that we can wrire a generalised expression for X^n + 1 / X^1/n

rajan edu

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1 Jun 2007 00:16:47 IST

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problem has been edited please as well as posted as corrected problem.

incomplte info is regretted pl.

Rajan

CyBorG

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Joined: 6 Jan 2007

Posts: 706

1 Jun 2007 11:59:46 IST

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Given 2cosA=x+1/x

So x²-2xcosA+1=0

So x=cosA

isinA where i=

-1

Let us consider x=cosA+isinA=cisA

So x³=cos3A+isin3A=cis3A (From De Moivre's theorem)

and 1/x³=cis(-3A)

So x³+1/x³=cos3A+isin3A+cos(-3A)+isin(-3A)

=2cos3A

Similarly we can show that xⁿ+1/xⁿ=2cosnA

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