The cotangent function is not undefined there. Look at it again.
Find the equation of the normal to y = cosec(2x) at the point where x = pi/4.
Differentiating cosec(2x) = -2cot(2x)cosec(2x)
At x = pi/4, dy/dx = -2cot(pi/2)cosec(pi/2)
I am unable to get a value for the dy/dx of the tangent since cot(pi/2) is undefined! How should I continue or did I make any mistakes?
Thank you very much!