There is no brackets so I am not really sure what you want.
Are you asking for all real values of x given that: ??
I suppose that is what you want.
I keep getting a different answer but I'd trust wolfram|alpha over me.
This is not an identity for either
[1-sec 8x] /[1- sec4x] = tan8x / tan4x nor
(1 - sec^8(x)) / (1 - sec^4(x)) = tan^8(x) / tan^4(x)
See here : https://www.desmos.com/calculator/figbjj45d8
And here : https://www.desmos.com/calculator/mbarrthbsp