Plane trigonometry, by S.L. Loney.

354

TRIGONOMETRY.

n+4 n+2 n n-2
n+4 ~ *. o
~(12 2 2 - 2 2
+ (- 2 ) 2 (- 2 cos 0)4
1.2.3.4
n1+4 n+2 n n-2 n-4 n 6
2 2 '2' 2 2 2 )
(-2 cos0)~
+............... + (2 cos 0)..'. (-1)2.2cosnO
COS2 0
= [1 + 1] - [n(n-2)+(n+2).n]
COS4 9
+ C4[(n + 2).n. (- 2)n- 4) +(n +)(+ 2).n.(n-2)]
+...............+ ( 1)2.(2 cos 0).
Hence, finally, when n is even,
/ \ ^ n2 COS20 n2(n2 - 29
(- 1)2 cos nO = 1 - c + os 0
n2 (n2 - 22)(2 42) os +..
+( 1)2 2n-1 co 0....................(3).
N.B. As before, the equations (2) and (3) of this article are only the
series (2) of Art. 294 written backwards.
*#297. From equation (2) of Art. 295 and equation (2) of Art. 296 we have, if n be odd,
2- sin nO n2 - 12 (2- 212)(n2 32)
(-1)2 -=1- cos20+ — cos0
(n2_ 12) (2 - 32) (n2 5) co +...
16
- -
+(- ) 2 (2 cos 0) -1+......(1),