Question

If A = 60° and B = 30°, verify that sin (A – B) = sin A cos B – cos A sin B.

Answer 1

sin (A – B) = sin 30°

= `1/2`

sin A cos B – cos A sin B = sin 60° cos 30° – cos 60° sin 30°

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

= `(3/4 - 1/4)`

= `2/4`

= `1/2`

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