Question

Show sin A - sin B = 2 cos ((A+B)/2) sin ((A-B)/2)

Answer 1

hi @SinYeeEr , do you know the formula for cos (x+y) and sin (x-y)

Answer 2

@hartnn yes! Any relationship?

Answer 3

Cos (x+y) = cos x cos y - sin x sin y
Sin ( x-y) = sin x cos y - cos x sin y

Answer 4

sorry for late reply @SinYeeEr
yes, those are correct,
if you put them in this(right side) :
2 cos ((A+B)/2) sin ((A-B)/2)
= 2 (cos A/2 cos B/2 - sinA/2 sin B/2 ) (sin A/2 cos B/2- cos B/2 sin A/2)

now foil these (multiply them out), if you simplify it correctly, you should get left side.
if you get stuck, you can always get back to me :)