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.

Related questions
See all questions in Proving Identities
Impact of this question
30048 views around the world
You can reuse this answer
Creative Commons License