Lagrange's trigonometric identities
Encyclopedia
In trigonometry
, Lagrange's trigonometric identities, named after Joseph Louis Lagrange
, are:
Setting
and equating the imaginary parts of both sides gives the first identity; equating the real parts of both sides gives the second.
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
, Lagrange's trigonometric identities, named after Joseph Louis Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...
, are:
Derivation
Lagrange's trigonometric identities may be derived by starting with the complex sumSetting
and equating the imaginary parts of both sides gives the first identity; equating the real parts of both sides gives the second.