1) sin(π/3 - α) + sin(2π/3 - α) = sin(π/3)*cosα - sinα*cos(π/3) + sin(2π/3)*cosα - sinα*cos(2π/3) = (√3*cosα)/2 - 0.5*sinα + (√3*cosα)/2 + 0.5*sinα = √3*cosα
2) 2cos(α+β)*cos(α-β) - 1 + 2sin^2(β) = 2*(cosα*cosβ - sinα*sinβ)*(cosα*cosβ + sinα*sinβ) - 1 + 2sin^2(β) = 2*(cosα*cosβ)^2 - 2*(sinα*sinβ)^2 - sin^2(β) - cos^2(β) + 2sin^2(β) = cos^2(β)*(2cos^2(α) - 1) + sin^2(β)*(1 - 2sin^2(α)) = cos(2α)*cos^2(β) + sin^2(β)*cos(2α) = cos(2α)*(cos^2(β) + sin^2(β)) = cos(2α)