485 
sin R” W ein Ks cos WL-cos RWeos RL 
See ee ~ gin R’L sin RW sin RL 
¢ sn RWsin W cos WL -cosR"W eos R"L 
sin RL sin Rk” W sin R"L 
or, substituting for cos RL, cos R"L the values— 
cos RW cos WL - sin RW sin WL cos W, 
cos R” W cos WL +sin R"W sin WL cos W, 
the expression becomes 
cos NR sin W 
sin RL sin R’L 
sin R” W digs : 3 
= RW (cosWL sin? RW+ sin WL sin RWeos RW cos W) 
sin RW 
+ ain kW 
(cosWL sin? R” W-sin WL sin R" Weos R" W cos W) 
cos NR sin W 
sn RL sin kh" L 
x {2cosWL sin R Wein R’W+sinWL sin (R'W-E W)cosW} 
_ Cos NR sin W sin WL 
~ gn RE sn kR'L ~ 
x {2 cot WLsin RWsin R"W+ sin (R"W- RW) cos W}. 
Or, putting for cot WL its value, which gives 
cot WL sin RWein R'W =sin? NW tan WR’, 
and putting also 
sin (R"W- RW) =sn2NW = 2 sin NW cos NW, 
the expression becomes 
_ 2008 NR sin Wsin WL sin? NW 
sin RL sin R"L 
The right-hand side of the equation to be proved is 
sin NW 
cos WR’ sin ‘sin NR 
(tan WR’ + cot NW cos W). 
sn Rk” LR —; cos R'U' sin U’, 
and we have 
