Question

Let $x=\cos a+i\sin a$ then the value of $x^n+\frac{1}{x^n}$ is

• A. $2i\sin na$
• B. $2\cos na$
• C. $0$
• D. none of these

Answer 1

The correct option is B $2\cos na$

Given,

$x=\cos a+i\sin a$.

Now,

$x^n$

$=(\cos a+i\sin a{)}^n$

$=\cos na+i\sin na$ [ Using De Movire's theorem].....(1)

And $\frac{1}{x^n}$

$=\frac{1}{\cos na+i\sin na}$

$=\cos na-i\sin na$.....(2).

Now adding (1) and (2) we get,

$x^n+\frac{1}{x^n}$

$=2\cos na$.