If x + frac{1}{x} = 2,cos theta , then {x^3} | vedclass

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(b) We have $x + \frac{1}{x} = 2\cos 	heta $,

Now ${x^3} + \frac{1}{{{x^3}}} = {\left( {x + \frac{1}{x}} ight)^3} - 3x\frac{1}{x}\left( {x + \fr

Vedclass · Accepted Answer

$2\,\cos \,3	heta $

Vedclass · Answer

(b) We have $x + \frac{1}{x} = 2\cos 	heta $,

Now ${x^3} + \frac{1}{{{x^3}}} = {\left( {x + \frac{1}{x}} ight)^3} - 3x\frac{1}{x}\left( {x + \frac{1}{x}} ight)$ 

$=  {(2\cos 	heta )^3} - 3(2\cos 	heta ) = 8{\cos ^3}	heta - 6\cos 	heta $

$=  2(4{\cos ^3}	heta - 3\cos 	heta ) = 2\cos 3	heta $. 

Trick : Put $x = 1$ $ \Rightarrow $ $	heta = {0^\circ }$. 

Then ${x^3} + \frac{1}{{{x^3}}} = 2 = 2\cos 3	heta $.

If $x + \frac{1}{x} = 2\,\cos \theta ,$ then ${x^3} + \frac{1}{{{x^3}}} = $

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