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

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(B) Given that $x + \frac{1}{x} = 2\cos 	heta$.We use the algebraic identity $a^3 + b^3 = (a + b)^3 - 3ab(a + b)$.Substituting $a = x$ and $b = \frac

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$2\cos 3	heta $

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(B) Given that $x + \frac{1}{x} = 2\cos 	heta$.We use the algebraic identity $a^3 + b^3 = (a + b)^3 - 3ab(a + b)$.Substituting $a = x$ and $b = \frac{1}{x}$,we get:${x^3} + \frac{1}{{{x^3}}} = {\left( {x + \frac{1}{x}} ight)^3} - 3\left( {x \cdot \frac{1}{x}} ight)\left( {x + \frac{1}{x}} ight)$$= {(2\cos 	heta )^3} - 3(1)(2\cos 	heta )$$= 8\cos^3 	heta - 6\cos 	heta$$= 2(4\cos^3 	heta - 3\cos 	heta)$Using the trigonometric identity $\cos 3	heta = 4\cos^3 	heta - 3\cos 	heta$,we obtain:$= 2\cos 3	heta$.

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

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