Question

If $n$ is an integer, prove that
$\cos (n\pi +\theta )={(-1)}^n\cos \theta$

Answer 1

$\cos (n\pi +\theta )=\cos n\pi \cos \theta -\sin n\pi \sin \theta =(-1{)}^n\cos \theta -0\sin \theta =(-1{)}^n\cos \theta$