Question

If A = 60⁰ and B = 30⁰, verify that: 
(i) sin (A – B) = sin A cos B – cos A sin B

Answer 1

sin (A-B)= sin `30^0 = 1/2`

sin A cos B - cos A sin B = sin `60^0 cos 30^0 - cos 60^0 sin 30^0`

=` (sqrt(3)/2 xx sqrt(3)/2 - 1/2 xx1/2 ) =(3/4 - 1/4) = 2/4 =1/2`

∴ sin (A – B) = sin A cos B – cos A sin B