Answer
$x = \frac{\sqrt{3}}{2}$
Work Step by Step
$sin^{-1}~x+tan^{-1}~\sqrt{3} = \frac{2\pi}{3}$
$sin^{-1}~x+\frac{\pi}{3} = \frac{2\pi}{3}$
$sin^{-1}~x = \frac{\pi}{3}$
$x = sin~ \frac{\pi}{3}$
$x = \frac{\sqrt{3}}{2}$
Trigonometry (10th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
0321671775
ISBN 13:
978-0-32167-177-6
Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 280: 36
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