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Definitions from Trigonometric integrals

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[DEFINITION]

Tangent and secant

The identities used to integrate $\int \tan^m x \sec^n x \, dx$ are

1+\tan^2 x=\sec^2 x,\qquad \frac{d}{dx}\tan x=\sec^2 x,\qquad \frac{d}{dx}\sec x=\tan x\sec x.

The two derivative identities are why $u=\tan x$ and $u=\sec x$ match a leftover factor of $\sec^2 x$ or $\tan x\sec x$ .

[1]: $\int \tan x \, dx$ and $\int \sec x \, dx$
[2]:Powers of tangent and secant
[3]:Trigonometric integrals

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Tangent and secant