When A + B + C = pi (angles of a triangle), special identities hold: (1) tanA + tanB + tanC = tanAtanBtanC, (2) cotAcotB + cotBcotC + cotC*cotA = 1, (3) sin2A + sin2B + sin2C = 4sinAsinBsinC, (4) cos2A + cos2B + cos2C = -1 - 4cosAcosBcosC, (5) $sin^{2A}$ + $sin^{2B}$ + $sin^{2C}$ = 2 + 2cosAcosBcosC. The derivation technique: use C = pi - A - B and expand using compound angle formulas. Identity (1) is derived from tan(A+B) = -tanC, expanding the LHS. These identities allow simplification of expressions involving triangle angles without knowing the specific angle values.