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

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Mathematics

Lexi Lang

26 April, 22:57

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

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Tanner · Answer 1

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