Cambridge O Level Additional Mathematics · Syllabus 4037 · Trigonometry
Pythagorean Identities
What is Pythagorean Identities?
The three Pythagorean identities supplied in the Additional Mathematics 4037 formula list 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 O Level Additional Mathematics.