University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.5 - Derivatives of Trigonometric Functions - Exercises - Page 152: 52


$$\lim_{x\to0}\sin\Big(\frac{\pi+\tan x}{\tan x-2\sec x}\Big)=-1$$

Work Step by Step

$$A=\lim_{x\to0}\sin\Big(\frac{\pi+\tan x}{\tan x-2\sec x}\Big)$$ $$A=\sin\Big(\frac{\pi+\tan 0}{\tan0-2\sec0}\Big)$$ $$A=\sin\Big(\frac{\pi+0}{0-\frac{2}{\cos0}}\Big)$$ $$A=\sin\Big(\frac{\pi}{-\frac{2}{1}}\Big)$$ $$A=\sin\Big(-\frac{\pi}{2}\Big)=-1$$
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