PLANE TRIGONOMETRY. C9 



320. From the identity 



(x-b)(x-c) (x-b)(x-a) (x-a)(x-b) 

 a (a-b)(a-c) c)(b-a) (c-a)(c-b)~ 



deduce the identities 



sinj-^sin^ + + =cos 



1 sin a - - 



sin (a ft) sin (a 



321. Prove the identity 



B y a 8 

 cos(/3 + y-a-8) sin -=-* sin 5 



R-y v-a . a- . S-a . 8-0 . 8-y 

 = 8sin^-^8inL- 8 in -^ sin sin -^ sin -^ . 



III. Inequalities. 



1 . Prove that cot > 1 -f cot for values of betv. 

 and TT. 



:i. Prove that, for real values of *, *," -=- ^ lies 



1-ooea , 1 + coea 

 betweeo . -5, and --;. 

 l-co8)3 1+coe/J 



324. If a?, y, z be any real quantities, and A, , C the angles 

 of a triangle, 



2yzcoBA +2zx cos B + 2xy cos C, 



