This is the basic and conceptual question from trigonometric ratios in which we have given sin (A – B) = 1/2 and cos (A + B) = 1, 0° ≤ (A + B) ≤ 90° and A > B and we have to find the value of angle A and B.
RS Aggarwal, Class 10, chapter 11, question no 24.
sin(A−B)=1/2
or sin(A−B)=sin30∘
A−B=30∘....(1)
Again, cos(A+B)=1/2
=cos60∘
A+B=60∘....(2)
Solving (1) and (2), we get
2A=90∘ or A=45∘
Putting A=45∘ in (1), we get
45∘−B=30∘
or B=45−30∘
=15∘
Therefore, A=45∘,B=15∘.