Trigonometric Identities
Trigonometric identities are equations involving the
trigonometric functions
that are true for every value of the variables involved.
Some of the most commonly used trigonometric identities are derived from the
Pythagorean Theorem
, like the following:
There are also the
reciprocal identities
:
The
quotient identities
:
The
co-function identities
:
The
even-odd identities
:
The
Bhaskaracharya
sum and difference formulas
:
The
double-angle formulas
:
(These are really just special cases of Bhaskaracharya's formulas, when
.)
The
half-angle or power-reducing formulas
:
(Again, a special case of Bhaskaracharya.)
The
sum-to-product formulas
:
And the
product-to-sum formulas
: