Let unit vectors aA and aB denote the directions of vectors A and B in the xy-plane that make angles α and β, respectively, with the x-axis.
a) Obtain a formula for the expansion of the cosine of the difference of two angles, cos (α − β), by taking the scalar product aA ·aB.
b) Obtain a formula for sin (α − β) by taking the vector product aB × aA.
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