In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are See more

These are also known as the angle addition and subtraction theorems (or formulae).
The angle difference identities for $${\displaystyle \sin(\alpha -\beta )}$$ and $${\displaystyle \cos(\alpha -\beta )}$$ can be derived from the … See more

The product-to-sum identities or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems. Historically, the first four of these were known as Werner's formulas, after Johannes Werner who used them for … See more

These identities, named after Joseph Louis Lagrange, are:
A related function is the Dirichlet kernel:
A similar identity is
The proof is the … See more

By examining the unit circle, one can establish the following properties of the trigonometric functions.
Reflections See more

Multiple-angle formulae
Double-angle formulae
Formulae for twice an angle.
• $${\displaystyle \sin(2\theta )=2\sin \theta \cos \theta =(\sin \theta +\cos \theta )^{2}-1={\frac {2\tan \theta }{1+\tan ^{2}\theta }}}$$ See more

For some purposes it is important to know that any linear combination of sine waves of the same period or frequency but different phase shifts is also a sine wave with the same period … See more