If sin(A+B) =1 and cos(A-B)= √3/2, 0°< A+B ≤ 90° and A> B, then find the measures of angles A and B.

 If sin(A+B) =1 and cos(A-B)= √3/2, 0°< A+B ≤ 90° and A> B, then find the
measures of angles A and B.

given sin(A+B) =1=sin(90 degrees)

so

 A+B =90degreees-------------(1)

given cos(A-B)= √3/2=cos(30 degrees)

 

A-B = 30 degrees-----------------(2)

 

now solve the two equations

 

adding the two equations gives 2A =120 or A = 60 degrees

 

substitute in the first equation to get B= 30 degrees 

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