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[fortpost]

4cosx · cosy = (e^ix + e^-ix)(e^iy + e^-iy) = e^i(x+y) + e^i(x-y) + e^-i(x-y) + e^-i(x+y)
4sinx · siny = (e^ix - e^-ix)(e^iy - e^-iy)/i² = -e^i(x+y) + e^i(x-y) + e^-i(x-y) - e^-i(x+y)
4cosx · cosy - 4sinx · siny = e^i(x+y) + e^i(x-y) + e^-i(x-y) + e^-i(x+y) + e^i(x+y) - e^i(x-y) - e^-i(x-y) + e^-i(x+y) = 2e^i(x+y) + 2e^-i(x+y) = 4cos(x+y)