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

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  1. Where is the equal sign?

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  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

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

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  4. Check that carefully Kelly !

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