How to Work Both Sides of a Trig Identity
Sum-to-Product Identities
Rearrange the Pythagorean Identities

Reciprocal Trigonometry Identities

The simplest and most basic trig identities (equations of equivalence) are those involving the reciprocals of the trigonometry functions. To jog your memory, a reciprocal of a number is 1 divided by that number — for example, the reciprocal of 2 is 1/2. Another way to describe reciprocals is to point out that the product of a number and its reciprocal is 1.


The same goes for the trig reciprocals.

Here’s how the reciprocal identities are defined:


In true fashion, when you multiply the reciprocals together, you get 1:


There’s always the warning, though, that the function can’t be equal to 0; the number 0 doesn’t have a reciprocal. The reciprocal identity is a very useful one when you’re solving trig equations. If you find a way to multiply each side of an equation by a function’s reciprocal, you may be able to reduce some part of the equation to 1 — and simplifying is always a good thing.

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