Question

Complete the identify
sin(a + b)cos b - cos(a + b)sin b

Answer 1

Where is the equal sign?

Answer 2

sin (a+b) = sin a cos b + cos a sin b
cos (a+b) = cos a cos b - sin a sin b
multiply the first by cos b
multiply the second by -sin b
then add them
and you get
sin a cos^2 b + cos a sin b cos b
-cos a cos b sin b + sin a sin^2 b

low and behold that is
sin a [ cos^2 b + sin^2 b ]
but we know cos^2 + sin^2 = 1
so we end up with
sin a

Answer 3

That just worked out too well to be true. I wonder if I made a mistake.

Answer 4

Check that carefully Kelly !