290 NEW SERIES for the 
To the fides of this equation let are correfponding fides of the 
equation 
I =if I 
tanA” 2 ‘tantA 
—tanzA } 
be added; then we get 
I iat a 
tan? At ae hiaa <A 
I rt ._ r+tan’A _ fec*A 
ee. tan? A . tanA” tan?A © tan3A 
yas A 
, and fimilarly, 
: : eer lf 7A 3 
tan? 4 A = sit ak tan? + Has alio tan - + tan A= 
r nk a I 21 z - 
tan = A(r-+tan 3 A) Stan - A fec 5 A: therefore, by fubfti- 
tuting, we get 
fechi A =~ tec SA I I 
fan? 5A StantczA g tan = A fects A. 
24. From this formula, by fubftituting a, 2 a, 42 ate — 
for A, and multiplying the fucceflive refults by the fractions 
a I < , : 
I, o> gists Gow We deduce the following feries of equations, 
the number of which is 7: 
fec’ a 
tan3 a 
—)-§ (tan = A+ tan} =A). 
