Quotient identities

The quotient relation of two trigonometric functions with another trigonometric function is called quotient trigonometric identity, simply called as quotient identity.


One trigonometric function can be divided by another trigonometric function mathematically but the quotient form them can also be a trigonometric function in some cases in trigonometry. The quotient relations of trigonometric functions are known as quotient identities and used as formulas in mathematics.

There are two quotient trigonometric identities in trigonometry mathematics.

Sine and Cosine with Tangent

The quotient of sine function by cosine function at an angle is equal to tangent function at the same angle.

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

Cosine and Sine with Cotangent

The quotient of cosine function by sine function at an angle is equal to cotangent function at the same angle.

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

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