Answer
See below.
Work Step by Step
1. Let $sin^{-1}v=x$, we have $sin(x)=v, cos(x)=\sqrt {1-v^2}$
2. Let $cos^{-1}v=y$, we have $cos(y)=v, sin(y)=\sqrt {1-v^2}$
3. $sin(x+y)=sin(x)cos(y)+cos(x)sin(y)=(v)(v)+(\sqrt {1-v^2})(\sqrt {1-v^2})=1$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.5 Sum and Difference Formulas - 6.5 Assess Your Understanding - Page 510: 101
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