How do you factor the expression and use the fundamental identities to simplify sec^4x-tan^4x?

1 Answer
Nghi N
Feb 19, 2017

(1 + sin^2 x)/(cos^2 x)

Explanation:

S = sec^4 x - tan^4 x = (sec^2 x - tan^2 x)(sec^2 x + tan^2 x)
The first factor is equal to 1 -->
sec^2 x - tan^2 x = 1/(cos^2 x) - sin^2 x/(cos^2 x) =
= (1 - sin^2 x)/(cos^2 x) = 1
Develop the second factor -->
1/(cos^2 x) + sin^2 x/(cos^2 x) = (1 + sin^2 x)/(cos^2 x)
Finally,
S = (1 + sin^2 x)/(cos^2 x)

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