Question

4) Is cos(θ - π) the same as cos(θ + π) for all values of θ?

Answer 1

@-pi is 180o from @,
@+pi is 180o away in the other direction, ending up where the first did.

These angles are the same so their cos are the same.

Answer 2

\[\cos \left( \theta-\pi \right)=\cos \left\{ -\left( \pi-\theta \right) \right\}=\cos \left( \pi-\theta \right)=-cos \theta \]
\[\cos \left( \pi+\theta \right)=-\cos \theta \]
hence both are same.