The identity sin1 x cos1 x P,2 Figure 1.69 establishes the identity for 0 6 x 6 1. To establish it for the rest of 3-1, 1], verify by direct calculation that it holds for x = 1, 0, and -1. Then, for values of x in (-1, 0), let x = -a, a 7 0, and apply Eqs. (3) and (5) to the sum sin-1 (-a) + cos-1 (-a).
The identity sin1 x cos1 x P,2 Figure 1.69 establishes the identity for 0 6 x 6 1. To establish it for the rest of 3-1, 1], verify by direct calculation that it holds for x = 1, 0, and -1. Then, for values of x in (-1, 0), let x = -a, a 7 0, and apply Eqs. (3) and (5) to the sum sin-1 (-a) + cos-1 (-a).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The identity sin1 x cos1 x P,2 Figure 1.69 establishes the identity for 0 6 x 6 1. To establish it for the rest of 3-1, 1], verify by direct calculation that it holds for x = 1, 0, and -1. Then, for values of x in (-1, 0), let x = -a, a 7 0, and apply Eqs. (3) and (5) to the sum sin-1 (-a) + cos-1 (-a).
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