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 (C) �(D) 5/4

sinc+sind=2 [sin(c+d)/2] [cos (c-d)/2]

sin2a+sin2b=2sin(a+b)*cos(a-b)

2sin(a+b) * cos(a-b) = 1/2 —–(1)

cos2a+cos2b=3/2

cosc+cosd=2 [cos(c+d)/2] [cos (c-d)/2]

cos2a+cos2b=2cos(a+b)*cos(a-b)

2cos(a+b) * cos(a-b) = 3/2 —–(2)

squaring and adding (1) and (2) we get,

4sin^2(a+b) * cos^2(a-b) + 4cos^2(a+b) * cos^2(a-b) = 9/4+1/4

4 cos^2(a-b) [sin^2(a+b)+cos^2(a+b)] = 10/4

cos^2(a-b) = 10/16

cos^2(a-b) = 5/8

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