Need help with this numerical analysis / scientific computing question. Program can be written using MATLAB or Python

2. The function fi (ao, ) sin(xo + h)-sin(m) can be transformed into another form, f2(zo, h), using the trigonometric formula - 2 cos Thus, f and f2 have the same values, in exact arithmetic, for any given argument values xo and h. a) Derive f2(o,h) b) Suggest a formula that avoids cancellation errors for computing the approximation (f(ao+1)-f()/h to the derivative of f (x) sin(x) at z . Write a MATLAB program that implements your formula and computes an approximation of f,(1.2), for le 20, 1e-19, . . . , 1