Question

what is the limit of (1-tanx)/(sinx-cosx) as x approaches pi/4?

Answer 1

Use l'Hôpitals rule:

if the value is indeterminate (0/0 or ∞/∞) at the limit, find the value of the derivative of the numerator divided by the derivative of the denominator.
in this case, try to evaluate
d(1-tan(x))/dx / d(sin(x)-cos(x))
as x approaches π/4. It is the negative of a simple irrational number.