Question 1039994
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cos(A-B)-sin(A+B)
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cos(A-B) = cos(A)*cos(B) + sin(A)*sin(B),     (1)


sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B)      (2)


(see any textbook on or including Trigonometry, &nbsp;or the lesson in this site &nbsp;<A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A>). 
Taking the difference of &nbsp;(1)&nbsp; and &nbsp;(2), &nbsp;you get


cos(A-B) - sin(A+B) = cos(A)*cos(B) + sin(A)*sin(B) - sin(A)*cos(B) - cos(A)*sin(B) = 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= cos(A)*(cos(B)-sin(B)) + sin(A)*(sin(B)-cos(B)) = (cos(A)-sin(A))*(cos(B)-sin(B)).


The solution by the other tutor is wrong.