Double angle formulas follow from compound angle formulas with B = A: sin(2A) = 2sinAcosA, cos(2A) = cos^2A - sin^2A = 2cos^2A - 1 = 1 - 2sin^2A, tan(2A) = 2tanA/(1-tan^2A). The three equivalent forms of cos(2A) are crucial — choose based on which ratio you want to eliminate. Rearranging gives half-angle formulas: cos^2(A/2) = (1+cosA)/2, sin^2(A/2) = (1-cosA)/2, tan(A/2) = sinA/(1+cosA) = (1-cosA)/sinA. Triple angle formulas: sin(3A) = 3sinA - 4sin^3A, cos(3A) = 4cos^3A - 3cosA. The Weierstrass substitution t = tan(x/2) expresses sin(x) = 2t/(1+t^2) and cos(x) = (1-t^2)/(1+t^2), converting trig equations to algebraic ones.