what is the derivative of x/tan(x) and find f'(pi/4)

Question

f'(x)=(tanx-x*sec(x)^2)/(tanx)^2
That's the quotient rule for derivatives or as my teacher says:

Low,low, low D'High, minus High d'low all over low square that's the quotient rule. It's a song which helps. D'High or d'low means the derivative of the top or bottom.

Anyways: the answer choices are:
2,1/2,1+pi/2,pi/2-1, 1-pi/2

and i keep getting 1-pi/8. This question is from an AP test in 1985 so i don't think they made a mistake in these answers.

deriv = (1*tan x - x sec^2 x)/tan^2 x

so for x= pi/4

deriv = (1 - pi/4(2))/1
=1 - pi/2, which was one of the choices

Answer 1

1-pi/2 appears to be correct.