Is the function #f(x) = 2 cot x# even, odd or neither?

1 Answer
Nov 14, 2015

Answer:

#2cot(x)# is an odd function.

Explanation:

A function #f(x)# is even if and only if #f(-x) = f(x)#
A function #f(x)# is odd if and only if #f(-x) = -f(x)#

Note that #sin(x)# is an odd function and #cos(x)# is even.

Thus we have
#f(-x) = 2cot(-x) = 2cos(-x)/sin(-x)#

Because sine is an odd function and cosine is even, we have

#f(-x)= 2cos(x)/(-sin(x)) = -(2cos(x)/sin(x)) = -f(x)#

Thus #2cot(x)# is odd.