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
