Answer
The identity is verified.
$arcsin(-x)=-arcsin~x$
Work Step by Step
Let $x=sin~y$, then $y=arcsin~x$.
We know that $sin(-y)=-sin~y$ because $sin~y$ is odd. So, $-x=sin(-y)$. Then:
$arcsin(-x)=-y=-arcsin~x$
Algebra and Trigonometry 10th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
9781337271172
ISBN 13:
978-1-33727-117-2
Chapter 6 - 6.6 - Inverse Trigonometric Functions - 6.6 Exercises - Page 487: 130a
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