Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises - Page 66: 70

Answer

$tan(sin^{-1}x) = \frac{x}{\sqrt {1-x^{2}}}$

Work Step by Step

$tan(sin^{-1}x)$ = $\frac {sin(sin^{-1}(x))}{cos(sin^{-1}(x))}$ $sin(sin^{-1}(x))$=$x$ $cos(sin^{-1}(x))$=$\sqrt{1-sin^2(sin^{-1}(x))}$=$\sqrt{1-x^2}$ $tan(sin^{-1}x)$ = $\frac{x}{\sqrt {1-x^{2}}}$
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