Answer
$-1$
Work Step by Step
$\lim_{x\to0}sin(\frac{\pi+tan(x)}{tan(x)-2sec(x)})=sin(\frac{\pi+tan(0)}{tan(0)-2sec(0)})=sin(\frac{\pi}{-2})=-1$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 3: Derivatives - Section 3.5 - Derivatives of Trigonometric Functions - Exercises 3.5 - Page 142: 52
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