Plane trigonometry, by S.L. Loney.

412 TRIGONOMETRY. [EXS. LXI.]
cos (a+ 2,3) cos (a +4)3).
5, cos a - +...... ad inf.
cosh2a cosh 3a
6. l + cosh a + - +3 +.....- ad inf.
sinh 2a sinh 3a.
7, sinha+2- + - +-...... ad mf.
12
8. l+ecosacos (sinl a) + 1 e2COa cos (2 sin a)+...... ad inf.
e2 sin a e3 sina
9. l+enacos (cos a)+ os (2 cos a) + cco (3cosa)......
ad inf.
5 cos 0 7 cos 30 9 cos 50
10. - - +...... ad inf.
[In the following examples c may be assumed to be positive and not
greater than unity; when c equals unity there will be, as in Art. 355,
exceptional cases for some values of the angle a.]
c2 C3
11. c sin a - sin 2a + sin 3a -...... ad inf.
2 3
3 1 1
12. c sina - c3 sin 3a + c5 sin 5a +.... ad inf.
3 5
13. c cos a + c3 cos 3a + c5 cos 5a+...... ad inf.
I 3
14. c cos a - c3 cos 3a + 1 c5 cos 5a +.... ad inf.
3 5
15. c sin a - c3 sin 3a + - c5 sin 5a +....... ad inf.
3 5
16. cos cos 5a -...... ad inf.
o 5
17. c cosa- c3cos(a+ 5 (a+ 43)...... ad inf.
1 1
18. sin a sin p + sin 2asin 23 + sin3asin 33...... adinf.
19. m sin2 a m2 sin22a + m3 sin2 3a...... ad inf.
2 3
1 1
20. sinh a - sinh2a sinh3a-...... ad inf.
2 3