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,...

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).