How do you simplify sec^4x-tan^4x?

1 Answer
Nghi N
Jan 8, 2017

1 + 2tan^2 x

Explanation:

sec^4 x - tan^4 x = (sec^2 x - tan^2 x)(sec^2 x + tan^2 x)
Since
(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;
sec^4x - tan^4 x = sec^2 x + tan^2 x
Reminder: sec^2 x = (1 + tan^2 x)
Finally,
sec^4 x - tan^4 x = 1 + 2tan^2 x

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