Question

if x+1/x= 2cos θ  then show that x^n +1/x^n= 2cos n θ 

Answer 1

Here we are going to use some concepts of Complex Numbers.


$\cos \theta + i \sin \theta = e^{i \theta} \\ \\ \\ \cos n\theta + i \sin n\theta = e^{i n\theta}$

Using these two concepts we split up the given statement, and we realize that the solution is:

$x = e^{i \theta}$
Then we just take the LHS of the statement we have to prove, and using the Euler Form, the question becomes quite simple.


The complete solution is in the image.