Sec8x-1/sec4x-1=tan8x/tan2x prove thatBy using trigonometric identities?

Dear Student,
Please find below the solution to your problem.

use secx = 1/cosx
now by using this we get,
(1- cos8x) (cos4x)/(1- cos4x)(cos8x)
use the formula of cos2x = 1-2 sin2x, we get
2 sin24x * cos4x/ 2sin22x* cos8x
now use 2 sinx cosx= sin2x, we get
sin 8x* cos2x/cos8x* sin2x
tan8x/tan2x

Thanks and Regards