Pythagorean Identities

What is Pythagorean Identities?

The three Pythagorean identities supplied in the Cambridge IGCSE Additional Mathematics 0606 List of formulas are sin squared A plus cos squared A equals one, sec squared A equals one plus tan squared A, and cosec squared A equals one plus cot squared A. The second is obtained by dividing the first through by cos squared A and the third by dividing it through by sin squared A, so all three carry the same content. An identity is true for every angle at which both sides are defined, which is why the second requires cos A to be non-zero and the third requires sin A to be non-zero. Their practical use is to replace a squared trigonometric term so that an equation contains only one trigonometric function.

This definition is part of the Trigonometry chapter in Cambridge IGCSE Additional Mathematics.

Concepts related to Pythagorean Identities

• common domain
• rearrangement
• reduction to one function
• proof