"please follow all the instructions before attempting this question, other wise I don't upvote you"

1) please write in python.

2)**this is very important*** please explain all steps of your algorithm in comments

3) ****this is also very important*** please do every part of this question.

4) provide the screenshot of test run of code.

5) Do not direct copy from chegg or any other internet resources.

you can take more than 2 hours ,i don't mind but algorithm should be correct

Question 2 Suppose we have two functions cos(x)and In(1+x) represented as Taylor series, cos(x) = 1 - + +... - In(1 + x) = x - + ... = *****Let f(x) =cos(x) and g(x) =In(1+x)**** Write the following functions in python : 1) Cosine_coeff(n) : returns the coefficient of x^n in the Taylor series of f (x). (Hint: coefficient of x^n is 0 when n is odd number) >>>Cosine_coeff(3) 0.0 2) log_coeff(n) : returns the coefficient of x^n in the Taylor series of g (x) >>>log_coeff(4) -0.25 3) mul_coeff(n): returns the coefficient of x^n in the Taylor series of f(x)*g(x) (Hint--First try this out by hand, then write the code after having figured out the pattern.) >>>mul_coeff(2) -0.5 4) diff_coeff(n): returns the coefficient of x^n in the Taylor series of d.f(x) dx (Hint: here you have to differentiate f(x) and then find coefficient of x^n >>>diff_coeff(3) 0.1666666667