Product identities


The mathematical relation between two trigonometric functions in product form is called the product identity of the trigonometric functions.

right angled triangle

In trigonometry, six functions are defined on the basis of the ratio of any two sides of a right angled triangle but three pairs of trigonometric functions have a relation in product form and they are called the product identities of trigonometric functions.


For example, if theta is an angle of a right angled triangle, here is the list of the possible product identities of the trigonometric functions.


Relation between Sine and Cosecant

$\large \sin{\theta} \csc{\theta} = 1$


Relation between Cosine and Secant

$\large \cos{\theta} \sec{\theta} = 1$


Relation between Tangent and Cotangent

$\large \tan{\theta} \cot{\theta} = 1$

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