423 
• 0 
sm - 
2_ 
sin L 
sm r , L _ i cos L — - sin L 
sm 
sm 
2 
\/S 
2 2 
£ _ 
2=^/3 C ot £-1 
6 2 2 
2 sin ^ 
-yi cot l= i+ — - 
sin — 
2 
2 sin £ 
Let tan 3 a = ^ — 
• d) 
sm jl 
sin ? sin 30° sin 0. 
Therefore ^3 cot P=l+tan 2 a— 
cos 2 a 
and tan L =^ 3 cos 3 a = tan 60° cos 2 a. 
But we have seen that 
. 0 . 0 
• T) sm - sm - 
sm P o , . 9 
= i andsmP- 
sin 90° sin L * " sin L 
Also from spherical triangle G^c^ we have 
cos G x a x = cos OjO cos oa x + sin G x o sin oa x cos 0 1 o^ 1 ; 
or cos_p 3 =cos 54° 44' cos P+sin 54° 44' sin P cos (120° + P). 
cos 54° 44' cos P-sin 54° 44' sin P cos (60° — L). 
— cos P [cos 54° 44'— sin 54° 44' tan P cos (60°-P)l . 
Let tan j3 = tan P cos (60°— L). 
Therefore cosjp 3 =cos P {cos 54° 44'— sin 54° 44' tan j3} 
C0S P {cos 54° 44' cos j3-^sin 54° 44' sin j3} 
cos_p 3 = 
cos /3 
cos P 
cos (54° 44' + j3). 
cos /3 
Also in spherical triangle G-^ea^ 
sin sin a x e sin^ 3 __ 
sm 
. — — t ui — - ~ * 
sm sm eP 1 ct 1 sin 90° sin (45° — A 3 ) 
sin *£. 
and sin (45° — A 0 ) = 
° sinp 3 
