Question

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

Answer 1

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.