If sin 2a + sin 2b = 1/2 and cos 2a + cos2b = 3/2, then cos^2(a-b) is equal to

(A) 3/8

(B) 5/8 [correct answer]

(C) ¾

(D) 5/4

Please give the solution for this question..

Thank you for your attempt to this question. It really helped me. 

The only thing is, the rest of the solution is correct but I think that you have done some mistake in the last line of the solution (regarding the identity of trigonometry used) and by correcting that error I get the answer as 5/8...which is probably the correct answer.