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.

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

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