If #2costheta=x+1/x# then prove that the value of the #x^n+1/(x^n), ninN# is #2cosntheta#?
3 Answers
Please see the explanation below.
Explanation:
By complex numbers,
Let
By Demoivre's theorem
For
Given
We get
By sridharacharya's formula we get
When
then
So
[by De Moivre's Theorem.]
And similarly
Hence adding we get
Similarly we get the same result when
By de Moivre's identity we know
then
then