Involution exponential formula ($e^{-i\theta A}=\cos \theta I-i\sin \theta A$)

For a linear operator with $A^2=I$, every even power is $I$ and every odd power is $A$. Separating the absolutely convergent matrix exponential series into those powers proves the displayed identity without a Hermiticity assumption. If $A$ is also a Hermitian operator, the exponential is a unitary operator.