# Quotient Trigonometric identities

## Definition

The quotient that represents a trigonometric function by the division of a trigonometric function by another trigonometric function is called the quotient relation of trigonometric functions.

In trigonometry, a trigonometric function can be divided by another trigonometric function and the quotient of them is also a trigonometric function. Hence, it is called the quotient identity of trigonometric functions.

They are two types of quotient laws in trigonometry and here is all of them in mathematical form to use them as trigonometric formulas in mathematics.

01

### Sine and Cosine Quotient Rule

The quotient of the division of sine of an angle by the cosine of same angle is tangent of that angle.

$\large \dfrac{\sin \theta}{\cos \theta} \,=\, \tan \theta$

02

### Cosine and Sine Quotient Rule

The quotient of the division of cosine of an angle by the sine of same angle is cotangent of that angle.

$\large \dfrac{\cos \theta}{\sin \theta} \,=\, \cot \theta$