Let r1 and r2 be unit vectors in the xy plane making angles a and R with the positive x-axis.
(a) Prove that r1= cos a i + sin a j, r2 = cos (b i + sin b j .
(b) By considering r1. r2 prove the trigonometric formulas
cos (a - b) = cos a cos b + sin a sin b, cos (a + b) = cos a cos b - sin a sin b
where a= alpha, b= beta
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