Angle sum identities are mathematical formulas that express the sine, cosine, and tangent of the sum of two angles in terms of the sines and cosines of the individual angles. For example, the identity for sine states that sin(A + B) = sin(A)cos(B) + cos(A)sin(B). These identities are useful in trigonometry for simplifying expressions and solving equations involving angles. These identities also apply to the difference of angles, providing similar formulas for sin(A - B), cos(A - B), and tan(A - B). Understanding these identities is essential for various applications in mathematics, physics, and engineering, where angle relationships are crucial.