From the given equation, using the cosine subtraction formula, we get cos(A-B) = 1 - sin(A)sin(B)sin(C).

The given equation can be rewritten as cos(A-B) = 1 - sinA sinB sinC.

If C = 90 degrees, then sinC = 1 and the equation becomes cos(A-B) = 1 - sinA sinB. Then cos(A-B) + sinA sinB = 1, which means cosAcosB = 1.

Since cosA and cosB are both less than or equal to 1, the only way for cosAcosB=1 is when cosA=1 and cosB=1, implying A=0 and B=0, which is impossible in a triangle.

If C = 90 degrees, A = B = 45 degrees and therefore a:b:c = 1:1:\sqrt 2, which confirms the equation holds