5.4 Sum and Difference Formulas
sin(u + v) = sin u cos v + cos u sin v
sin(u - v) = sin u cos v - cos u sin v
cos(u + v) = cos u cos v - sin u sin v
cos(u - v) = cos u cos v + sin u sin v
tan(u + v) = (tan u + tan v)/(1 - tan u tan v)
tan (u - v) = (tan u - tan v)/(1 + tan u tan v)
sin(u - v) = sin u cos v - cos u sin v
cos(u + v) = cos u cos v - sin u sin v
cos(u - v) = cos u cos v + sin u sin v
tan(u + v) = (tan u + tan v)/(1 - tan u tan v)
tan (u - v) = (tan u - tan v)/(1 + tan u tan v)
Sum and difference formulas can be used to find exact values of trigonometric functions involving sums or differences of special angles.
Evaluating a Trigonometric Function
Evaluating a Trigonometric Expression
Applying a Sum Formula
Proving an Identity
Sum and difference formulas can be used to derive reduction formulas involving expressions
sin(θ + (nπ/2)) and cos(θ + (nπ/2))
where n is an integer.
Deriving Reduction Formulas
sin(θ + (nπ/2)) and cos(θ + (nπ/2))
where n is an integer.
Deriving Reduction Formulas
Solving a Trigonometric Equation