Verify the identity algebraically.
sec2x = sec2 x/2-sec2x
sec2x = sec^2 x/2-sec^2x
1 /cos2x = sec^2x/ [2- sec^2x] and we can write
cos2x /1 = [2 - sec^2x] / sec^2x
cos2x = 2/sec^2x - sec^2x/sec^2x
cos2x = 2/sec^2x - 1
cos2x = [2/1] / [1/cos^2x] -1
cos2x = 2cos^2x - 1 which is true
