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.

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

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