G2 BOOK OF MATHEMATICAL PROBLEMS. 



884 If tan2a = 2 



then will tan (a - B) be equal to -- : or to - - . 



a-d b+c 



285. If tan(< + a), tan<, tan (< + ) be in A. p. then will 

 cot a, tan <, cot ft be in A. p. 



286. If a, ft y be all unequal and less than 2-n; and if 



cos a + cos ft + cos y = sin a + sin {$ + sin y = ; 



o 



then will cos a a 4- cos 2 ft 4- cos 2 y = sin a a + sin 2 ft + sin 2 y = . 



tan 26 tan 2v 



287. Having given - r = -^- ; prove that each 



tan (y + a) tan (a + /3) 



member of the equation is equal to 



tan 08 + y)' 



and that sin 2 (ft + y) + sin 2 (y 4- a) + sin 2 (a 4- ft) = 0, 

 unless tan (ft - y) = 0. 



288. Prove that 



-^X 1 **?) *-=; 



289. If 



C = 2 cos - 5 cos 8 0+4 cos s $, S = 2 bin - 5 sin 8 6 + 4 sin 5 ; 

 then will 

 C cos 30 4- Sain 30 = cos 20, and tfcos 30- Csin 30 = - ^sin 20. 



22 



290. Having given 



if 



x cos </> 4- y sin < = x cos <' 4- y sin </>' = 2a, and 2 cos J cos ^ = 1 ; 



J J 



prove that 7/ a = 4.a (a - x) ; </>, <#>' leing unequal and less than 2rr. 



