Question
Prove by vector method that sin (A – B) = sin A cos B – cos A sin B
Solution
Let OX and OY be two axes and let 
be unit vectors along OX and OY respectively.
Let
be two vectors such that
so that
Draw
be the unit vector along z-axis.
Now,
and
Also,
...(2)
From (1) and (2), we get
be unit vectors along OX and OY respectively.Let
be two vectors such that so thatDraw
be the unit vector along z-axis.Now,
and
Also,
...(2)From (1) and (2), we get
