Question

Find acute angles A and B, if cos (2-B)=sin(A+2B)=root3/2

Answer 1

cos (2 A - B) = sin (A + 2 B) = √3 / 2

=> 2A - B = 30°    --- (1)
        and   A+2B = 60°     ---- (2)

(1) * 2 + (2)  =>   5 A = 120°
=>  A = 24°
=>  B = 18°