Lim x-> pi/4 of (1-tanx)/(sinx-cosx)

To evaluate the expression Lim x-> pi/4 of (1-tanx)/(sinx-cosx), the first thing to do is to substitute x with pi/4. In this case, the answer is 0/0 or indeterminate. using L'hopital's rule, we derive separately the numerator and the denominator resulting to 1- sec2 x / (cos x + sin x). substituting again, the answer is -1/sqrt 2