"Maclaurin series expansion for the basic trigonometric functions sin(x), cos(x), and tan(x)" Can this work for other trigonometric functions such as sec, csc, and cot? Why or why not?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 78E
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"Maclaurin series expansion for the basic trigonometric functions sin(x), cos(x), and tan(x)"

Can this work for other trigonometric functions such as sec, csc, and cot? Why or why not?

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