Unless (which I don't think is true), I think there was a mistake in the question you got.
... from previous poster. Continue as follows:
= (1 - sin²A).(1-sin²B) - sin²A.sin²B (sorry can't use greek letters !)
= 1 -sin²A - sin²B + sin²A.sin²B - sin²A.sin²B
= 1 -sin²A - sin²B
= sin²A + cos²A - sin²A - sin²B
= cos²A - sin²B
The question as written asked for the RHS to be cos²A - sin²A which is, of course, incorrect !
Good luck,
M