Consider the function f : JR ) R defined by x) = cos"(m), where n is an even integer. It can be shown that any positive power of cos x can be expressed as a sum of multiples of terms of the form 003093). where the k are non-negative integers. Note that the term where k = D is the constant term. It can also be shown that any odd positive power of sin a; can be expressed as a sum of multiples of terms of the form sinUm), where the k are non-negative integers. (a) What is the constant term in the expansion of f() described above? @ yntax advice: Remember to use correct Maple syntax. For example. . the factorial 1;! may be written as n! or factorial (n) n . the binomial coefficient ( k) may be written as binomial (n. k] m - the term a. is written a'x {b} Now, consider the function g : R > JR defined by 9(m) = 3i3967($)f($)- Briefly explain in words why 9(m) may be written as a sum of multiples of terms of the form sin(km). where k are non-negative integers. Essay box advice: In your explanation. you don't need to use exact Maple syntax or use the equation editor. as long as your expressions are sufficiently clear for the reader. For example. you can write sin(k.1:) as 'sinlkXJ'. and sin967(m)f(m) as 'sin"967{x) f(x}'. :3: [%[[@Q;::: ::|=:::: i-ozmn and;3125ef Words: I] A (c) In the above expansion of 9(3). which of the following terms have zero coefficients? Multiple selection advice: In a multiple selection question. marks are deducted for incorrect selections {but you cannot get less than zero}. You are advised to only select options that you are sure about