Question

sin(a)-icos(a)?=cos(a-pi/2)+isin(a-pi/2)

Answer 1

\[\cos\left(a-\frac{\pi}{2}\right)=\cos a\cos\frac{\pi}{2}+\sin a\sin\frac{\pi}{2}=\sin a\]
Likewise,
\[\sin\left(a-\frac{\pi}{2}\right)=\sin a\cos\frac{\pi}{2}-\sin\frac{\pi}{2}\cos a=-\cos a\]
which establishes the identity.