Editing Trigonometric functions (section)

===Derivatives and antiderivatives===
The [[derivative]]s of trigonometric functions result from those of sine and cosine by applying the [[quotient rule]]. The values given for the [[antiderivative]]s in the following table can be verified by differentiating them. The number&nbsp;{{mvar|C}} is a [[constant of integration]].

{| class="wikitable" style="text-align: center;"
!<math>f(x)</math> !! <math>f'(x)</math> !! <math display="inline">\int f(x) \, dx</math>
|-
|<math>\sin x</math>||<math>\cos x</math>||<math>-\cos x + C</math>
|-
|<math>\cos x</math>||<math>-\sin x</math>||<math>\sin x + C</math>
|-
|<math>\tan x</math>||<math>\sec^2 x</math>||<math>\ln \left| \sec x \right| + C</math>
|-
|<math>\csc x</math>||<math>-\csc x \cot x</math>||<math>\ln \left| \csc x - \cot x \right| + C</math>
|-
|<math>\sec x</math>||<math>\sec x \tan x</math>||<math>\ln \left| \sec x + \tan x \right| + C</math>
|-
|<math>\cot x</math>||<math>-\csc^2 x</math>||<math>-\ln \left| \csc x \right| + C</math>
|}
Note: For <math>0<x<\pi</math> the integral of <math>\csc x</math> can also be written as <math>-\operatorname{arsinh}(\cot x),</math> and for the integral of <math>\sec x</math> for <math>-\pi/2<x<\pi/2</math> as <math>\operatorname{arsinh}(\tan x),</math> where <math>\operatorname{arsinh}</math> is the [[inverse hyperbolic sine]].

Alternatively, the derivatives of the 'co-functions' can be obtained using trigonometric identities and the chain rule:

:<math>
\begin{align}
\frac{d\cos x}{dx} &= \frac{d}{dx}\sin(\pi/2-x)=-\cos(\pi/2-x)=-\sin x \, , \\
\frac{d\csc x}{dx} &= \frac{d}{dx}\sec(\pi/2 - x) = -\sec(\pi/2 - x)\tan(\pi/2 - x) = -\csc x \cot x \, , \\
\frac{d\cot x}{dx} &= \frac{d}{dx}\tan(\pi/2 - x) = -\sec^2(\pi/2 - x) = -\csc^2 x \, .
\end{align}
</math>