Mathematics

Problem

Consider

h(x)=\cot(kx)

, where

k

is a non-zero real constant. a. Express

h(x)

using only

\sin(kx)

and

\cos(kx)

. b. Find

h'(x)

and simplify your answer completely in terms of cotangent or cosecant functions, as appropriate. c. For

k=3

, evaluate

h'(\tfrac{\pi}{6})

and state its exact value.