functions. This tance of complex analysis, mentioned at Problem Set 12.7 1. Prove that cos z, sin 2, cosh 2, sinh z are entire functions, 2. Verify by differentiation that Re cos z and Im sin z are harmonic, Compute (in the form w+lo) 3. cos (1.7+ 1.50 6. cos 10/ 9. cos 3mi 4. sin (1.7 +1.50 7. sin (V2-40) 10. sin (3 + 2) 5. sin 10/ 8. cos (m) 11. cos (2.10.20) 12. Show that cosh cosh x cos y + sinh x sin y, sinh r sinth x cos y 1 cosh x sin y. Compute (in the form u + i) 13. cosh (-2+30) 14. sinh (4 – 3) 15. sinh (2 đ Find all solutions of the following equations. 16. cosh z0 17. cos z=31 18. sinz 1000 1. sin r = i sinh 1 20. sin cosh 3 21. cosh z = 22. Find all values of z for which (a) cos z, (b) sin z has real values. 23. Obtain cosh (-1.5+ 1.7) from (15) and the answer to one of the above problems. 24. Find Re tan z and Im tan z. 25. Prove that cos z is even, cos (-2) = cos z. and sin z is odd, sin (-2) sin z. 26. Show that cos zsin (z+) and sin (2) sin z, as in real. 27. Show that sinh z and cosh z are periodic with period 2m. 28. From (9) and (15) derive the addition rules cosh (2) cosh z, cosh sinh, sinh sinh ( + y) - sinh z, cosh ty + cosh tự sinh tạ 29. Prove cos + sin z=1, coshez – sinh: z=1, cos zsin³ z = cos 2 coth® z + sinh" z = cosh 22. 30. Show that sinh yllcos zs cosh y and [sinh yl s Isin z cosh y. Conclude that the complex cosine and sine are not bounded in the whole complex plane.