trig proofs?

Question

well this one got me stumped

Sec4x-Tan4x

the 4s are superscripted

Answer 1

(sec x)^4 - (tan x)^4
= [(sec x)^2 - (tan x)^2][(sec x)^2 + (tan x)^2]

***(sec x)^2 = (tan x)^2 + 1 then (sec x)^2 - (tan x)^2 = 1

(sec x)^4 - (tan x)^4
= (sec x)^2 + (tan x)^2

Answer 2

What are you trying to prove?
sec^4x - tan^4x
( sec ² x - tan ² x )( sec ² x + tan ² x )____(a)
Now sin ² x + cos ² x = 1 so
tan ² x + 1 = sec ² x
__(a) becomes :-
( 1 )( tan ² x + 1 + tan ² x )
2 tan ² x + 1
Hope this is what you are after.