# Reciprocal identities

The reciprocal relation of a trigonometric function with another trigonometric function is called reciprocal identity.

## Introduction

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

### Sine and Cosecant functions

Sin function is a reciprocal function of cosecant and cosecant function is also a reciprocal of sine function.

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

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

### Cosine and Secant functions

Cos function is a reciprocal function of secant and secant function is also a reciprocal of cosine function.

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

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

### Tangent and Cotangent functions

Tan function is a reciprocal function of cotangent and cot function is also a reciprocal of tangent function.

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

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

Email subscription
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more