Question

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

• A. $\cos 3\theta$
• B. $2\cos 3\theta$
• C. $\frac{1}{2}\cos 3\theta$
• D. $\frac{1}{3}\cos 3\theta$

Answer 1

The correct option is B $2\cos 3\theta$

$x^3+\left(\frac{1}{x^3}\right)=(x+(\frac{1}{x}){)}^3-3x\times (\frac{1}{x}\left)\right(x+\left(\frac{1}{x}\right))=(2cos\theta {)}^3-3\left(2cos\theta \right)=8co{s}^3\theta -6cos\theta =2[4co{s}^3\theta -3cos\theta ]=2cos3\theta$