how do you calculate cos 67.5 using the cos2A=1-2COS^2A ? or is there any easier way ?
Note that 2*67.5 = 135, and that cos 135 = -cos 45, and that cos 45 = 1/sqrt(2)
So set A = 67.5 and use your formula (noting that cos 67.5 will be positive).
But note that your formula is incorrect!!
cos2A is 2cos^2(A) - 1, not 1 - 2cos^2(A)
