Double angle formulas follow from compound angle formulas with B = A: sin(2A) = 2sinAcosA, cos(2A) = $cos^{2A}$ - $sin^{2A}$ = 2$cos^{2A}$ - 1 = 1 - 2$sin^{2A}$, tan(2A) = 2$\frac{tanA}{1-tan^2A}$. 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$$\frac{A}{2} = $\frac{1+cosA}{2}$, sin^2$$\frac{A}{2} = $\frac{1-cosA}{2}$, tan$\frac{A}{2}$ = $\frac{sinA}{1+cosA}$ = $\frac{1-cosA}{sinA}$. Triple angle formulas: sin(3A) = 3sinA - 4$sin^{3A}$, cos(3A) = 4$cos^{3A}$ - 3cosA. The Weierstrass substitution t = tan$\frac{x}{2}$ expresses sin(x) = 2$\frac{t}{1+t^2}$ and cos(x) = $\frac{1-t^2}{(1+t^2)}$, converting trig equations to algebraic ones.