Question

Show that :

i. sin A sin (B – C) + sin B sin (C – A) + sin C sin (A – B) = 0 

ii. sin (B – C) cos (A – D) + sin (C – A) cos(B – D) + sin(A – B) cos(C – D) = 0

Answer 1

i. sin A sin (B – C) + sin B sin (C – A) + sin C sin (A – B) = 0 

Take L.H.S,

sin A sin (B – C) + sin B sin (C – A) + sin C sin (A – B) 

Multiplying & Dividing by 2 :

= 0 

= R.H.S 

Hence Proved

ii. sin (B – C) cos (A – D) + sin (C – A) cos(B – D) + sin(A – B) cos(C – D) = 0

Take L.H.S ,

sin (B – C) cos(A – D) + sin (C – A) cos(B – D) + sin(A – B) cos(C – D) 

Multiplying & Dividing by 2 :

= 0 

= R.H.S 

Hence Proved