Find the derivative of (sec x − 1) (sec x + 1).

1.	Find the derivative of (sec x − 1) (sec x + 1).
Answer» Let, y = (sec x − 1) (sec x + 1) = sec²x − 1 = tan²x ∴ \(\frac{dy}{dy}=\frac{d}{dx}\,(tan^2\,x)\) \(=2\,tan\,x\frac{d}{dx}\,tan\,x\) \(=2\,tan\,x.sec^2\,x.\)

Answer»

Let,

y = (sec x − 1) (sec x + 1)

= sec²x − 1

= tan²x

∴ \(\frac{dy}{dy}=\frac{d}{dx}\,(tan^2\,x)\)

\(=2\,tan\,x\frac{d}{dx}\,tan\,x\)

\(=2\,tan\,x.sec^2\,x.\)

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