# Reciprocal Trigonometric identities

## Definition

A reciprocal relation of a trigonometric ratio with another trigonometric ratio at an angle is called reciprocal trigonometric identity.

One trigonometric ratio has a direct reciprocal relation with another trigonometric ratio mutually due to their definition by the lengths of same sides of the right angled triangle. But their definitions are in reciprocal form and valid for all the angles. Therefore, the reciprocal relations of trigonometric ratios are called reciprocal trigonometric identities in trigonometry.

### List of reciprocal identities

The six trigonometric ratios form three reciprocal trigonometrical identities in trigonometry by the reciprocal relation. Assume, the angle of the right angled triangle is theta ($\theta$) to express the reciprocal relation between trigonometrical identities in mathematical form.

1

#### Sine and Cosecant

Sine is reciprocal to cosecant and vice-versa due to definition of them by the lengths of opposite side and hypotenuse of a right angled triangle at an angle.

Learn Proof
2

#### Cosine and Secant

Cosine is reciprocal to secant and vice-versa due to definition of them by the lengths of adjacent side and hypotenuse of a right angled triangle at an angle.

Learn Proof
3

#### Tangent and Cotangent

Tangent is reciprocal to cotangent and vice-versa due to definition of them by the lengths of opposite side and adjacent side of a right angled triangle at an angle.

Learn Proof