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This article lists mathematical identities, that is, identically true relations holding in mathematics. Bézout's identity (despite its usual name, it is not, properly speaking, an identity) Binet-cauchy identity
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
A left identity element that is also a right identity element if called an identity element. The empty set ∅ {\displaystyle \varnothing } is an identity element of binary union ∪ {\displaystyle \cup } and symmetric difference , {\displaystyle \triangle ,} and it is also a right identity element of set subtraction ∖ : {\displaystyle ...
Signs of trigonometric functions in each quadrant. All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4.
In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes. The following is a compilation of the notable of these, many of which are used for computational purposes.
Hypergeometric function lists identities for the Gaussian hypergeometric function; Generalized hypergeometric function lists identities for more general hypergeometric functions; Bailey's list is a list of the hypergeometric function identities in Bailey (1935) given by Koepf (1995). Wilf–Zeilberger pair is a method for proving hypergeometric ...
In mathematics, the triple bar is sometimes used as a symbol of identity or an equivalence relation (although not the only one; other common choices include ~ and ≈). [ 7 ] [ 8 ] Particularly, in geometry , it may be used either to show that two figures are congruent or that they are identical. [ 9 ]