10. The function fl (x,8) = cos(x+5)-cos(x) can be transformed into another form, f2(x,8), using the trigonometric formula cos()-cos(y)--2 sin 2 Thus, fi and f2 have the same values, in exact arithmetic, for any given argument values x and . (a) Show that, analytically, fi(x,8)/ or f2(x,)/ are effective approximations of the func- tion-sin(x) for sufficiently small. (b) Derive f2(x,8). (c) Write a MATLAB script which will calculate gi(x,8)-fi(x,8)/5+sin(x) and g2(x,8)- fig, )/5+ sin(x) for x-3 and -Le-11 . (d) Explain the difference in the results of the two calculations