Trigonometric function identity means that two or more functions in trigonometric function are equal. The following are common trigonometric function identities:

Basic identities of sine, cosine and tangent;

sin^2(x) + cos^2(x) = 1

tan(x) = sin(x) / cos(x)

1 + tan^2(x) = sec^2(x)

1 + cot^2(x) = csc^2(x)

Sum and difference formula:

sin(x y)= sin(x)cos(y)cos(x)sin(y)

cos(x y) = cos(x)cos(y)？ Sin (x) sin (y)

tan(x y)=(tan(x)tan(y))/( 1？ tan(x)tan(y))

Double angle formula:

sin(2x) = 2sin(x)cos(x)

cos(2x)= cos^2(x)-sin^2(x)= 2cos^2(x)- 1 = 1-2sin^2(x)

tan(2x)=(2tan(x))/( 1-tan^2(x))

Triple angle formula:

sin(3x) = 3sin(x) - 4sin^3(x)

cos(3x) = 4cos^3(x) - 3cos(x)

tan(3x)=(3tan(x)-tan^3(x)/( 1-3tan^2(x)

These trigonometric identities are very useful in solving trigonometric problems, computer graphics, physics, engineering and other fields. Knowing and mastering these identities can help us better understand the properties and applications of trigonometric functions.