PLANE TRIGONOMETRY. 63 



291. Having given 



(a; - a) cos 6 + y sin = (x - a) cos & + y sin ff = a, 



B & 



and tan - - tan - = 2ej 



prove that y*= 2ax - (1 -e 8 ) a?, 0, ff being unequal and less than IV. 



292. If (1 + sin 0) (1 + sin <) (1 + sin \j/) = cos cos < cos ^, 

 then will sec' + sec* < + sec'i/r - 2 sec sec < sec \j/ = 1. 



293. Having given 



cos A + cos B + cos (7+ cos A cos -5 cos (7 = 0; 

 prove that 



cosecM + cosec*^ + cosec 8 (7 2 cosec -4 cosec J? cosec (7=1. 



294. If 



tanM tan A' = tan* 5 tan B = tan*(7 tan C" = tan A tan 5 tan C, 

 and cosec 2-4 + cosec 2 + cosec 2(7 = j 



thru will 



>. Having given 



x sin 3 (ft - y) + y sin 3 (y - a) 4- z sin 3 (a - ft) = ; 

 prove that 



x sin (ft- y) 4- y sin (y ~ a) 4- z sin (a- /?) 

 X 006 (fi y) + y COS (y a) + Z 008 (a /:> > 



sin 2 (/J - y) 4- sin 2 (y-a)-f sin 2 (a-/?) 

 + COS 2 (/? - y) 4- Cos 2 (y - a) 4- cos 2 (a^/3) ~ 



296. Having given the equations 



y f = y* + a* - 2ya cos^>, + ^4-^ = 



prove )8y sin + ya sin <f> + aj8 sin ^ = 0. 



