TRIGONOMETRY. 67 



\vo like equations between y, a, and a, ft respectively; 



that if 



. ft-y . y-a . a - 3 

 s,n E^J sin C sm -^ 



be finite, IT + C a -A'-A"-X" + 2AC' = 0. 



311. Eliminate from the equations 

 c 



312. Having given the equations 



A - A a++ m 



- tana = tan-^- tan/J = tan 



- -- = -- -- = 



that 

 bin (P + y) + sin (y + a) -f sin (a + /?) = 



in /? siny 1 



a, /?, y being unequal, 



and 



313. Prove that 



cos* 6 - 2 cos cos a cos (a + 6) + cos* (a -f 6) 

 is independent of 0. 



"11. Prove that 

 sin2a cos /J cosy sin (/? - y) + sin 2)9 cos y cos a sin (y - a) 



+ sin 2y cos a cos ft sin (a - ft) = 0, 



cos 2a cos/? coaysin(/3-y)+ + 



S sin (/? - y) sin (y - a) sin (a - ft). 



Prove that 



, W( . ,50 ,30) 

 [drfy-tin' 



= cos* + COB* 20 + cos* 3d - 3cos0 cos 26 cos 3d, 



3d r . 3d /id) 



( cos' 2--C08* j> 



sin* d + sin* 2d -f sin 8 3d - 3 sin d sin 2d sin 3d. 



52 



