Trigonometric Identities

Trigonometric identities (trig identities) are equalities that involve trigonometric functions that are true for all values of the occurring variables. These identities are useful when we need to simplify expressions involving trigonometric functions.

The following is a list of useful Trigonometric identities: Quotient Identities, Reciprocal Identities, Pythagorean Identities, Co-function Identities, Addition Formulas, Subtraction Formulas, Double Angle Formulas, Even Odd Identities, Sum-to-product formulas, Product-to-sum formulas.

Quotient Identities

Reciprocal Identities

Pythagorean Identities

Co-function Identities

Addition Formulas

sin (a + b) = sin a cos b + cos a sin b

cos (a + b) = cos a cos b – sin a sin b

Subtraction Formulas

sin (a - b) = sin a cos b - cos a sin b

cos (a - b) = cos a cos b + sin a sin b

Double Angle Formulas

sin 2a = 2 sin a cos a

cos 2a = cos 2a – sin 2a = 2 cos 2a – 1 =  1 – 2 sin 2a

Even-odd Identities

Sum-to-product Formulas

Product-to-sum Formulas

Half Angle Formulas

Videos

The following video describes the quotient, reciprocal and Pythagorean identities.

Fundamental trigonometric identities -
Professor Edward Burger explains fundamental trigonometric identities

Simplifying a trigonometric expression using trigonometric identities -
Professor Edward Burger explains simplifying a trigonometric expression using trigonometric identities

Using half-angle identities to solve a trigonometric equation -
Professor Edward Burger explains using half-angle identities to solve a trigonometric equation

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