Question

(sec 8 x - 1)/(sec 4x -1) = tan 8x/tan 4x Prove it!

Answer 1

One of the first things I usually do is test if the identity is true by picking any value of x.
Since it is an identity it should work for all value of x
let x=10
LS = (1/cos80 -1)/(1/cos40-1)
= appr 15.58

RS = tan80/tan40 = appr 6.758

so , not true, no point trying to prove it.