Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.6 Exercises - Page 373: 90

Answer

$${\text{False}}$$

Work Step by Step

$$\eqalign{ & {\arcsin ^2}x + {\arccos ^2}x = 1 \cr & {\text{Let }}x = \frac{{\sqrt 2 }}{2},{\text{ then}} \cr & {\arcsin ^2}x + {\arccos ^2}x = {\arcsin ^2}\left( {\frac{{\sqrt 2 }}{2}} \right) + {\arccos ^2}\left( {\frac{{\sqrt 2 }}{2}} \right) \cr & {\arcsin ^2}x + {\arccos ^2}x = {\left( {\frac{\pi }{4}} \right)^2} + {\left( {\frac{\pi }{4}} \right)^2} \cr & {\arcsin ^2}x + {\arccos ^2}x = \frac{{{\pi ^2}}}{8} \cr & {\text{Therefore, the statement is false}}{\text{.}} \cr} $$
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