How do you verify #Sec^4x-tan^4x=sec^2x+tan^2x#?

1 Answer
Nghi N.
Sep 13, 2016

Prove trig expression

Explanation:

Transform the left side of the expression:
#LS = sec^4 x - tan^4 x = (sec^2 x - tan^2 x)(sec^2 x + tan^2 x)#.
Since the first factor,
#(sec^2 x - tan^2 x) = (1/(cos^2 x) - (sin^2 x)/(cos^2 x)) =#
#= (1 - sin^2 x)/(cos^2 x) = (cos^2 x)/(cos^2 x) = 1#
There for, the left side becomes;
#LS = (sec^2 x + tan^2 x)#, and it equals the right side.

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