Course: Stochastic Calculus for finance Level 2

I have the partial solution to this question, but I need more detailed, step-by-step solution (including all missing steps in between).

The Question is:

The answer is :

Extra supporting formulas mentioned in the question:

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Proof. By (4.5.29), c(t, z) _ p(t,x) = z-e-r(T-t)K. So pz(t,x) = cz(t,x)-1 N(d+ (T-t,x))-1, = Proof For an agent hedging a short position in the put, since t-Pa(t,x)