Determine the limit of the trigonometric function:

Question

Limit as x approaches pi/4 of (1-tanx)/(sinx-cosx)
I need step by step help using the special trignometric limits theorem.

Answer 1

(1-tanx)/(sinx-cosx) = 0/0, so try LHospital's Rule:

-sec^2(x)/(cosx+sinx) = (-2)/(2/√2) = -2/√2 = -√2