cos(x)- = o (37), x 2, ~sin(x)-_o_xzj + 1 Given that and cos(a - b) - cos(a)cos(b) + sin(a)sin(b) [a Derive a Taylor series for cos(2x4)cos(*4)+ sin(2x^)sin(*') around x = 0. In Python b] Using your answer from [a], write a code which computes the Taylor series of cos(2x^)cos(x4) + sin(2x4)sin(r') using recursion, vectorization, and a tolerance based while loop approach. [c] On the interval [0, ], plot the semi-log error in your approximation for tolerance values 10-4, 10-6, and 10-8. Label axes and provide a legend for your graph cos(x)- = o (37), x 2, ~sin(x)-_o_xzj + 1 Given that and cos(a - b) - cos(a)cos(b) + sin(a)sin(b) [a Derive a Taylor series for cos(2x4)cos(*4)+ sin(2x^)sin(*') around x = 0. In Python b] Using your answer from [a], write a code which computes the Taylor series of cos(2x^)cos(x4) + sin(2x4)sin(r') using recursion, vectorization, and a tolerance based while loop approach. [c] On the interval [0, ], plot the semi-log error in your approximation for tolerance values 10-4, 10-6, and 10-8. Label axes and provide a legend for your graph