If $\cos A = \sin B$ , does $A+B = 90$ degrees? If $\cos A = \sin B$ , does $A+B = 90$ degrees?


My school teacher says that this works but I was unable to understand how. I have been unable to find a proof for this. How does this work?

Edit I should add that this is for an acute case
Sometimes a picture says more than 1000 words:
But this isn't the only solution.
$$\cos A=\sin(A+pi/2)=\sin B \implies B=A+\pi/2 +2k\pi$$
for $k=0$, $B=A+\pi/2  \iff B-A= \pi/2$.