F'(x) = [(cosx)(-sinx) - (1 + cosx)(-sinx)] / (cosx)^2
F'(x) = [-cosxsinx + sinx + sinx] / (cosx)^2
F'(x) = [-cosxsinx + 2sinx] / (cosx)^2
F'(x) = [sinx(2 - cosx)] / (cosx)^2