cos(82°)cos(37°)+sin(82°)sin(37°) expression is the right side of the formula cos(a-b) with particular values for a and b

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cos(82-37)=cos 45= sqrt 2/2
Since cos(α)cos(β) + sin(α)sin(β) = cos(α-β)

cos(82°-37°) = cos(45°) = [tex] \frac{ \sqrt{2}}{2} [/tex]