Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 388: 100


See the proof below.

Work Step by Step

We have $$y'=\sec y \Longrightarrow \frac{dy}{\sec y}=dx\Longrightarrow \cos y dy=dx.$$ Now, by integration we get $$\sin y =x+c.$$ When $x=0$, $y=0$, and the constant $c=0$. Hence, $$\sin y =x\Longrightarrow y=\sin^{-1}x.$$ This completes the proof.
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