# Reciprocal identities

The reciprocal relation between any two trigonometric functions is called a reciprocal identity.

## Introduction

Every trigonometric function has a reciprocal relation with another trigonometric function. So, the six trigonometric functions form six reciprocal trigonometric identities in trigonometry and they are used as formulas in mathematics.

#### Sine and Cosecant functions

Sine has a reciprocal relation with Co-secant function and also Cosecant function also has reciprocal relation with sine function.

$(1)\,\,\,\,\,\,$ $\sin{\theta} = \dfrac{1}{\csc{\theta}}$

$(2)\,\,\,\,\,\,$ $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

#### Cosine and Secant functions

Cosine function has a reciprocal relation with Secant function and also Secant function also has reciprocal relation with cosine function.

$(3)\,\,\,\,\,\,$ $\cos{\theta} = \dfrac{1}{\sec{\theta}}$

$(4)\,\,\,\,\,\,$ $\sec{\theta} = \dfrac{1}{\cos{\theta}}$

#### Tangent and Cotangent functions

Similarly, Tangent function has a reciprocal relation with Cotangent function and also Cotangent function also has reciprocal relation with Tangent function.

$(5)\,\,\,\,\,\,$ $\tan{\theta} = \dfrac{1}{\cot{\theta}}$

$(6)\,\,\,\,\,\,$ $\cot{\theta} = \dfrac{1}{\tan{\theta}}$