We often come across with functions in mathematics. A function f is co-function of a function g if f(A) = g(B) whenever A and B are complementary angles.
A mathematical function is said to be a special kind of relation between inputs and outputs, where every input value is connected with exactly one output value by the means of a particular property. The trigonometric functions are one of the most important ones.

Co-function Identities

$\sin θ = \cos (90 - θ)$ $\cos θ = \sin (90 - θ)$ $\tan θ = \cot (90 - θ)$ $\csc θ = \sec (90 - θ)$ $\sec θ = \csc (90 - θ)$ $\cot θ = \tan (90 - θ)$

Formula of Co-function

$\sin [\frac{π}{2} - θ] = \cos θ$ $\cos [\frac{π}{2} - θ] = \sin θ$ $\tan [\frac{π}{2} - θ] = \cot θ$ $\cot [\frac{π}{2} - θ] = \tan θ$ $\csc [\frac{π}{2} - θ] = \sec θ$ $\sec [\frac{π}{2} - θ] = \csc θ$ Trigonometric Co-Functions

	$\begin{array}{l} \sin θ \end{array}$	$\begin{array}{l} \cos θ \end{array}$	$\begin{array}{l} \tan θ \end{array}$	$\begin{array}{l} \csc θ \end{array}$	$\begin{array}{l} \sec θ \end{array}$	$\begin{array}{l} \cot θ \end{array}$
$\begin{array}{l} \sin θ \end{array}$	$\begin{array}{l} \sin θ \end{array}$	$\begin{array}{l} \pm \sqrt{1 - \cos^{2} θ} \end{array}$	$\begin{array}{l} \pm \frac{\tan θ}{\sqrt{1 + \tan^{2} θ}} \end{array}$	$\begin{array}{l} \frac{1}{\csc θ} \end{array}$	$\begin{array}{l} \pm \frac{\sqrt{\sec^{2} - 1}}{\sec θ} \end{array}$	$\begin{array}{l} \pm \frac{1}{\sqrt{1 + \cot^{2} θ}} \end{array}$
$\begin{array}{l} \cos θ \end{array}$	$\begin{array}{l} \pm \sqrt{1 - \sin^{2} θ} \end{array}$	$\begin{array}{l} \cos θ \end{array}$	$\begin{array}{l} \pm \frac{1}{\sqrt{1 + \tan^{2} θ}} \end{array}$	$\begin{array}{l} \pm \frac{\sqrt{\csc^{2} θ - 1}}{\csc θ} \end{array}$	$\begin{array}{l} \frac{1}{\sec θ} \end{array}$	$\begin{array}{l} \pm \frac{\cot θ}{\sqrt{1 + \cot^{2} θ}} \end{array}$
$\begin{array}{l} \tan θ \end{array}$	$\begin{array}{l} \pm \frac{\sin θ}{\sqrt{1 - \sin^{2}} θ} \end{array}$	$\begin{array}{l} \pm \frac{\sqrt{1 - \cos^{2} θ}}{\cos θ} \end{array}$	$\begin{array}{l} \tan θ \end{array}$	$\begin{array}{l} \pm \frac{1}{\sqrt{\csc^{2} θ - 1}} \end{array}$	$\begin{array}{l} \pm \sqrt{\sec^{2} θ - 1} \end{array}$	$\begin{array}{l} \frac{1}{\cot θ} \end{array}$
$\begin{array}{l} \csc θ \end{array}$	$\begin{array}{l} \frac{1}{\sin θ} \end{array}$	$\begin{array}{l} \pm \frac{1}{\sqrt{1 - \cos^{2} θ}} \end{array}$	$\begin{array}{l} \pm \frac{\sqrt{1 + \tan^{2} θ}}{\tan θ} \end{array}$	$\begin{array}{l} \csc θ \end{array}$	$\begin{array}{l} \pm \frac{\sec θ}{\sqrt{\sec^{2} θ - 1}} \end{array}$	$\begin{array}{l} \pm \sqrt{1 + \cot^{2} θ} \end{array}$
$\begin{array}{l} \sec θ \end{array}$	$\begin{array}{l} \pm \frac{1}{\sqrt{1 - \sin^{2} θ}} \end{array}$	$\begin{array}{l} \frac{1}{\cos θ} \end{array}$	$\begin{array}{l} \pm \sqrt{1 + \tan^{2} θ} \end{array}$	$\begin{array}{l} \pm \frac{\csc θ}{\sqrt{\csc^{2} θ - 1}} \end{array}$	$\begin{array}{l} \sec θ \end{array}$	$\begin{array}{l} \pm \frac{\sqrt{1 + \cot^{2} θ}}{\cot θ} \end{array}$
$\begin{array}{l} \cot θ \end{array}$	$\begin{array}{l} \pm \frac{\sqrt{1 - \sin^{2} θ}}{\sin θ} \end{array}$	$\begin{array}{l} \pm \frac{\cos θ}{\sqrt{1 - \cos^{2} θ}} \end{array}$	$\begin{array}{l} \frac{1}{\tan θ} \end{array}$	$\begin{array}{l} \pm \sqrt{\csc^{2} θ - 1} \end{array}$	$\begin{array}{l} \pm \frac{1}{\sqrt{\sec^{2} θ - 1}} \end{array}$	$\begin{array}{l} \cot θ \end{array}$

Co-function Identities

Formula of Co-function

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