The sum: $ 1+ {n \choose 1}\cos{\theta} + {n \choose 2}\cos{2\theta} + …. + {n \choose n}\cos{n\theta} $ equals

Question

The sum:

$$ 1+ {n \choose 1}\cos{\theta} + {n \choose 2}\cos{2\theta} + …. + {n \choose n}\cos{n\theta} $$ equals

Answer 1

It is the real part of ${(1+e^{i\theta})}^{n}$.

Answer 2

It is $2^n cos^n(\theta/2) \cos(n\theta/2).$