Question: Show that |sinh x| |cosh z| cosh x by using (a) Identity (12), Sec. 35; (12) |cosh z|2 = sinh2 x + cos2

Show that |sinh x| ≤ |cosh z| ≤ cosh x by using
(a) Identity (12), Sec. 35;
(12) |cosh z|2 = sinh2 x + cos2 y,
where z = x + iy. While these identities follow directly from definitions (1), they are often more easily obtained from related trigonometric identities, with the aid of relations (3) and (4).
(b) The inequalities |sinh y| ≤ |cos z| ≤ cosh y, obtained in Exercise 9(b), Sec. 34.

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