Step-by-step explanation:

Given, sin(A+B)=cos(A−B)=23

or, sin(A+B)=23

or, A+B=60o......(1).  [ Since A,B are acute]

Also given,

cos(A−B)=23

or, A−B=30o.......(2). [ Since A,B are acute]

Solving (1) and (2) we get,

A=45o,B=15o.

Answer:

A=60

B=60

Step-by-step explanation:

[tex] \sin \: a = \sqrt{ \frac{3}{2} } \\ \: \: \: \: \: \: a = 60° [/tex]

[tex] \tan \: b = \sqrt{3} \\ \: \: \: \: \: \: \: \: \: b = 60°[/tex]

[tex] \: \: \: \: \: \: \: \: \: \cos(a - b) = 1 \\ cos(60°-60°) = 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \cos0° = 1[/tex]

Hence Proved.....