Question

If $\frac{1}{x}+x=2cos\theta$, then $x^n+\frac{1}{x^n}$ is equal to

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given $\frac{x+x^{-1}}{2}=cos\theta$

This is valid for any x = $e^{i\theta }$

$\Rightarrow$ x = $e^{i\theta }$

$x^n+\frac{1}{x^n}=e^{in\theta }+\frac{1}{e^{in\theta }}$

= $2cos\left(n\theta \right)$